{"id":48,"date":"2026-07-06T11:42:28","date_gmt":"2026-07-06T10:42:28","guid":{"rendered":"https:\/\/idcmi.usm.md\/?page_id=48"},"modified":"2026-07-15T14:16:37","modified_gmt":"2026-07-15T13:16:37","slug":"laboratorul-algebra-si-topologie","status":"publish","type":"page","link":"https:\/\/idcmi.usm.md\/?page_id=48","title":{"rendered":"Laboratorul Algebr\u0103 \u0219i Topologie"},"content":{"rendered":"<div id=\"left\">\n<h3>Direc\u0163ii de cercetare<\/h3>\n<ul>\n<li>Algebra (teoria radicalilor, probleme de structura \u00een sisteme algebrice apropiate inelelor, modulelor \u015fi algebrelor);<\/li>\n<li>Quasigrupuri \u015fi analiza combinatorie (teoria general\u0103 a quasigrupurilor \u015fi opera\u0163iilor algebrice, probleme de combinatoric\u0103 \u00een quasigrupuri \u015fi aplica\u0163ii la codificarea \u015fi cifrarea informa\u0163iei);<\/li>\n<li>Logica matematic\u0103 (probleme algoritmice ale expresibilit\u0103\u0163ii func\u0163ionale precum \u015fi ale generaliz\u0103rilor ei \u00een logici neclasice);<\/li>\n<li>Algebra topologic\u0103;<\/li>\n<li>Geometria grupurilor discrete.<\/li>\n<\/ul>\n<h3>Proiecte \u00een derulare<\/h3>\n<p>&nbsp;<\/p>\n<h3>Arhiva proiectelor<\/h3>\n<ol>\n<li>Proiectul institu\u0163ional\u00a0<a href=\"http:\/\/www.math.md\/projects\/15.817.02.04F\/\" target=\"_blank\" rel=\"noopener\">&#8220;Tendin\u0163e moderne \u00een algebr\u0103, topologie \u015fi geometrie: cercet\u0103ri fundamentale \u015fi aplica\u0163ii&#8221;<\/a>, conduc\u0103tor \u2013 Ca\u015fu Alexei, CS\u015eDT, 2015-2019.<\/li>\n<li>Proiectul institu\u0163ional &#8220;Probleme actuale ale algebrei \u015fi ecua\u0163iilor diferen\u0163iale: aspecte teoretice \u015fi aplicative&#8221;, conduc\u0103tor \u2013 M. Popa, CS\u015eDT, 2011-2014.<\/li>\n<li>Proiectul institu\u0163ional \u201eCercet\u0103ri fundamentale \u00een structuri algebrice \u015fi calcule logice, aplica\u0163ii la codarea informa\u0163iei\u201d, conduc\u0103tor \u2013 M. Ra\u0163a, CS\u015eDT, 2006-2010.<\/li>\n<li>Proiectul institu\u0163ional &#8220;Aplicarea metodelor laticiale la cercetarea topologiilor \u00een grupuri \u015fi inele, torsiunilor \u00een module \u015fi variet\u0103\u0163ilor hiperbolice&#8221;, conduc\u0103tor A. Ca\u015fu, CS\u015eDT, 2006-2010.<\/li>\n<li>Proiectul interna\u0163ional &#8220;Algoritmi noi de autentificare a informa\u0163iei electronice \u015fi scheme criptografice de partajare a secretului&#8221;, conduc\u0103tor V. \u015ecerbacov, CS\u015eDT-\u0420\u0424\u0424\u0418, 2006-2010.<\/li>\n<li>Proiectul interna\u0163ional &#8220;Algebr\u0103 topologic\u0103 \u015fi diferen\u0163ial\u0103&#8221;, conduc\u0103tor V. Arnautov, CS\u015eDT-\u0420\u0424\u0424\u0418, 2006-2010.<\/li>\n<li>Cercetarea laticelor de radicali \u015fi de topologii \u00een grupuri, inele \u015fi module; conduc\u0103tor: V. Arnautov, 2004-2005.<\/li>\n<li>Cercetarea variet\u0103\u0163ilor sistemelor matematice \u00een algebr\u0103, logic\u0103, geometrie \u015fi topologie; conduc\u0103tor: Iu.Reabuhin, 2001-2003.<\/li>\n<li>Elaborarea \u015fi aplicarea unor metode algebrice generale \u00een teoria inelelor \u015fi grupurilor, \u00een logica matematic\u0103, topologie \u015fi geometrie; conduc\u0103tor: V. Arnautov, 2000-2002.<\/li>\n<li>MRDA-CRDF, BGP-I, MM2-3017 &#8220;Scheme de control digital pe baz\u0103 de quasigrupuri&#8221; \u2013 proiect comun cu matematicieni din Universitatea Statului Pennsylvania, S.U.A., 2001-2003, conduc\u0103tori: V.Izba\u015f, G. L. Mullen.<\/li>\n<li>MRDA-CRDF, BGP-II, MM1-3040, &#8220;Noi coduri \u015fi cifruri pe baz\u0103 de quasigrupuri&#8221; \u2013 proiect comun cu matematicieni din Universitatea Statului Pennsylvania, S.U.A., 2003-2005, conduc\u0103tori: V.Izba\u015f, G. L. Mullen.<\/li>\n<\/ol>\n<h3>Rezultate importante<\/h3>\n<h4>Algebr\u0103<\/h4>\n<p>Cercet\u0103rile \u00een domeniul algebrei (teoriei inelelor, algebrelor \u015fi modulelor) \u00een Institutul de Matematic\u0103 \u015fi Informatic\u0103 au fost ini\u0163iate \u00een anul 1961 de c\u0103tre fondatorul acestui institut, academicianul Vladimir Andrunachievici. \u00cen prezent cercet\u0103rile algebrice \u00een institut se efectueaz\u0103 sub conducerea acad. Iurie Reabuhin, iar printre cercet\u0103torii de baz\u0103 este doctorul habilitat \u00een \u015ftiin\u0163e fizico-matematice, profesor universitar A.Ca\u015fu. Tematica cercet\u0103rilor curente: teoria structural\u0103 a algebrelor local finit dimensionale, probleme de tip Burnside \u00een inele \u015fi algebre, teoria radicalilor \u015fi torsiunilor \u00een categorii de module.<\/p>\n<ul>\n<li>A fost ob\u0163inut\u0103 descrierea celor mai importante tipuri de operatori de \u00eenchidere (ereditari, maximali, minimali, coereditari) ai unei categorii de module \u00een limbajul submodulelor dense \u015fi (sau) a submodulelor \u00eenchise \u00een raport cu operatorul dat. (A. Ca\u015fu);<\/li>\n<li>a fost dezvoltat\u0103 teoria general\u0103 a radicalilor \u00een inele asociative \u015fi \u00een module; a fost ar\u0103tat\u0103 existen\u0163a radicalilor supernilpoten\u0163i \u015fi nespeciali (V.Andrunachievici, Iu.Reabuhin);<\/li>\n<li>a fost dezvoltat\u0103 teoria aditiv\u0103 a idealelor \u015fi a fost construit\u0103 teoria structural\u0103 a algebrelor, asociative \u00een zero (V.Andrunachievici, Iu.Reabuhin, R.Grigor);<\/li>\n<li>a fost construit un continuum de variet\u0103\u00e2i minime de inele (Iu.Reabuhin, R.Grigor);<\/li>\n<li>a fost clarificat\u0103 comportarea torsiunilor, localiz\u0103rilor \u015fi a laticelor de submodule \u00een situa\u0163ii de adjunc\u0163ie \u015fi \u00een Morita contexte cu ajutorul functorilor principali (A.Ca\u015fu);<\/li>\n<li>au fost g\u0103site construc\u0163ii generale ale algebrelor local nilpotente \u015fi local finit-dimensionale, au fost descrise variet\u0103\u0163ile marcate de algebre asociative; a fost ar\u0103tat\u0103 juste\u0163ea ipotezei lui Sestacov despre nilpoten\u0163a algebrelor (Gh.Cecanu).<\/li>\n<li>Au fost efectuate cercet\u0103ri \u00een domeniul algebrei (inele, module, categorii), \u00een special teoria radicalilor \u015fi torsiunilor \u00een categorii de module. (A.Ca\u015fu);<\/li>\n<li>Cu ajutorul unor preradicali de tip standard au fost introduse patru opera\u0163ii noi \u00een laticea submodulelor unui modul. Au fost ar\u0103tate propriet\u0103\u0163ile principale ale acestor opera\u0163ii, precum \u015fi unele rela\u0163ii ale lor cu opera\u0163iile laticeale, \u00een particular rela\u0163ii de distributivitate. (A.Ca\u015fu);<\/li>\n<li>A fost analizat\u0103 comportarea radicalilor \u015fi torsiunilor sub ac\u0163iunea functorilor principali, a fost studiat\u0103 laticea torsiunilor \u00een cazuri speciale (\u00een Morita contexte \u015fi \u00een situa\u0163ia de adjunc\u0163ie). A fost stabilit\u0103 rela\u0163ia dintre clase de module st\u00eengi \u015fi mul\u0163imi speciale de ideale st\u00eengi, au fost descrise clase importante de module (clase naturale, \u00eenchise, radicale, f\u0103r\u0103 torsiune, etc.) (A.Ca\u015fu);<\/li>\n<\/ul>\n<h4>Quasigrupuri \u015fi analiz\u0103 combinatorie<\/h4>\n<p>Cercet\u0103ri \u00een domeniul teoriei quasigrupurilor \u015fi \u00een domenii adiacente precum teoria re\u0163elelor algebrice, ecua\u0163ii func\u0163ionale \u015fi analiza combinatorie se efectueaz\u0103 \u00een cadrul Institutului de Matematic\u0103 \u015fi Informatic\u0103 \u00eencep\u00e2nd cu anul 1962. Fondator \u015fi conducator al cercet\u0103rilor \u015ftiin\u0163ifice \u00een aceast\u0103 direc\u0163ie a fost cunoscutul savant, profesorul universitar, Valentin Belousov (1925-1988). Direc\u0163iile actuale de cercetare \u0163in de problemele de centralitate a quasigrupurilor, de caracterizare a propriet\u0103\u0163ilor asocian\u0163ilor \u015fi a comutatorilor congruen\u0163elor quasigrupurilor, a izotopilor grupurilor, \u00een particular, a quasigrupurilor liniare, a n-quasigrupurilor separabile autoortogonale \u015fi a n-T-quasigrupurilor, a transversalelor de bucl\u0103 \u015fi a sistemelor unilaterale Stein, de cercetare a modalit\u0103\u0163ilor de aplicare a quasigrupurulor \u0103n teoria codurilor.<\/p>\n<ul>\n<li>Au fost elabora\u0163i criptoalgoritmi noi baza\u0163i pe dou\u0103 probleme dificile din teoria quasigrupurilor \u015fi \u00een baza lor au fost construite noi cifruri si coduri. A fost efectuat\u0103 criptoanaliza acestor cifrurilor ob\u0163inute \u015fi s-a demonstrat c\u0103 ele sunt mai rezistente dec\u00eet cifrurile cunoscute de acest tip la atacul brut \u015fi atacul pe baza cunoa\u015fterii criptogramei unui mesaj predeterminat. \u00cen S-sisteme de cuasigrupuri binare au fost gasite cuasigrupuri strict recursiv derivabile, pe baza lor au fost construite noi coduri MDS (Maximum Distance Separable). Aceste coduri corecteaz\u0103 erorile care apar la transmiterea informa\u0163iei. Au fost determinate valorile parametrilor codului care asigur\u0103 dimensiunea maximal\u0103 a codului. (G. Beleavscaia, V. Izba\u015f, V. \u015ecerbacov);<\/li>\n<li>s-a rezolvat problema despre existen\u0163a bazei finite pentru cvasiidentit\u0103\u0163ile de ranguri m\u0103rginite de acela\u015fi num\u0103r ale oric\u0103rei algebre finite. S-a ob\u0163inut c\u0103 bucla Moufang (A-bucle, CH-cvasigrupul, cvasigrupuri distributiv) rezolubil\u0103 ce verific\u0103 condi\u0163ia maximalit\u0103\u0163ii pentru subbucle este finit separabil\u0103 \u015fi, totodat\u0103, s-a demonstrat existen\u0163a unui algoritm de rezolvare a problemei de apartenen\u0163\u0103 a elementului subbuclei date. (Ursu V.);<\/li>\n<li>a fost \u00eembog\u0103\u0163it\u0103 substan\u0163ial teoria general\u0103 a quasigrupurilor, \u00een particular, aspectele ei ce \u0163in de caracterizarea autotopiilor (automorfismelor), nucleelor, centrului, congruen\u0163elor \u015fi submul\u0163imilor normale ale quasigrupurilor (V.Belousov, G.Beliavscaia, V.Izba\u015f);<\/li>\n<li>au fost puse bazele teoriei asociatorilor, comutatorilor \u015fi a asocian\u0163ilor quasigrupurilor (G.Beliavscaia);<\/li>\n<li>au fost caracterizate diferite clase de quasigrupuri \u015fi bucle printre care buclele Moufang, buclele Bol, IP-quasigrupurile, CI-buclele, quasigrupurile distributive (distributive la st\u00e2nga), TS-quasigrupurile, monoquasigrupurile \u015f.a. (V.Belousov, V.Izba\u015f, V.\u015ecerbacov);<\/li>\n<li>au fost puse bazele teoriei quasigrupurilor n-are \u015fi a algebrelor pozi\u0163ionale de quasigrupuri; au fost caracterizate sistemele de quasigrupuri cu identit\u0103\u0163i generalizate ale asociativit\u0103\u0163ii, medialit\u0103\u0163ii, tranzitivit\u0103\u0163ii, distributivit\u0103\u0163ii, Stein \u015f.a. (V.Belousov, G.Beliavscaia);<\/li>\n<li>au fost solu\u0163ionate o serie de ecua\u0163ii func\u0163ionale pe multimea opera\u0163iilor de quasigrup (V.Belousov);<\/li>\n<li>a fost elaborat\u0103 teoria general\u0103 a re\u0163elelor algebrice \u015fi a configura\u0163iilor acestora (V.Belousov, I. Leah );<\/li>\n<li>au fost solu\u0163ionate un \u015fir de probleme ce \u0163in: de aspectul combinatorial al quasigrupurilor ortogonale, conjugat ortogonale \u015fi autoortogonale (V.Belousov, P.S\u00eerbu); de admisibilitatea, inclusiv par\u0163ial\u0103, \u015fi ortogonalitatea par\u0163ial\u0103 a quasigrupurilor (G.Beliavscaia);<\/li>\n<li>au fost propuse unele modalit\u0103\u0163i noi de utilizare a quasigrupurilor \u00een teoria codurilor. Au fost descrise scheme de partajare a secretului, bazate pe sistemele ortogonale de opera\u0163ii partial sau complet \u015fi sistemele de opera\u0163ii n-are ce corespund schemelor de partajare a secretului. S-au determinat condi\u0163iile necesare \u015fi suficiente pentru existen\u0163a unui complement ortogonal al unui grupoid \u015fi s-a calculat num\u0103rul de complemen\u0163i ortogonali al unui grupoid (G.Beliavscaia, V.Izba\u015f, V.\u015ecerbacov);<\/li>\n<li>a fost elaborat aparatul algebric al transversalelor \u00een grupuri \u015fi bucle binare \u015fi grupuri n-are, ceea ce a permis s\u0103 fie generalizate unele rezultate cunoscute \u00een teoria grupurilor \u00een obiectele respective (E. Cuzne\u0163ov);<\/li>\n<li>au fost stabilite \u015fase clase de cuasigrupuri definite de seturi de parastrofi ale lor. Fiecare clas\u0103 este caracterizat\u0103 cu ajutorul a patru identit\u0103\u0163i cu dou\u0103 variabile. Au fost cercetate cuasigrupurile \u00een care to\u0163i \u015fase parastrofi sunt diferi\u0163i (DC-cuasigrupuri). S-a stabilit un criteriu c\u00e2nd un cuasigrup este DC-cuasigrup (DC-T-cuasigrup, DC-IP-cuasigrup). A fost demonstrat\u0103 existen\u0163a DC-T-cuasigrupurilor pentru orice num\u0103r natural n&gt;6 (G.Beliavscaia, T.Popovici);<\/li>\n<li>\u00een clasa opera\u0163iilor de acela\u015f tip sau de tipuri similare, definite pe o mul\u0163ime arbitrar\u0103, s-au determinat condi\u0163ii suficiente de izomorfism a opera\u0163iilor. S-au determinat unele ecua\u0163ii ce implic\u0103 ortogonalitatea unor opera\u0163iilor de anumit tip (V.Izba\u015f);<\/li>\n<li>au fost studiate leg\u0103turile \u00eentre transversalele \u00een bucle \u00een raport cu subbucle \u015fi a transversalelor \u00een grupurile multiplicative corespunz\u0103toare lor. Au fost demonstrate teoreme de structur\u0103 despre izomorfismul opera\u0163iilor de transversal\u0103. S-a stabilit un criteriu de existen\u0163\u0103 a transversalei de bucl\u0103 \u00een raport cu o subbucl\u0103. Au fost ob\u0163inute propriet\u0103\u0163ile transform\u0103rilor transversalelor buclei \u00een raport cu o subbucl\u0103 astfel \u00eenc\u00e2t opera\u0163iile de transversal\u0103 ob\u0163inute s\u0103 fie izomorfe (izotope). S-au cercetat propriet\u0103\u0163i ale transversalelor \u00een grupuri n-are, s-a generalizat teoremma lui Gluskin-Hossu \u00eentr-o clas\u0103 de bucle n-are (E. Cuzne\u0163ov, S. Botnari);<\/li>\n<li>au fost cercetate nucleele quasigrupurilor. Au fost ob\u0163inute condi\u0163ii de &#8220;normalitate&#8221; a congruen\u0163elor grupoizilor, grupoizilor cu diviziune de st\u00e2nga (de dreapta), grupoizilor cu reducere de st\u00e2nga (de dreapta). S-a demonstrat ca orice quasigrup paramedial finit este izomorf cu produsul direct al unui quasigrup paramedial cu un idempotent \u015fi al unui quasigrup care este un izotop al unui quasigrup distributiv.\u00cen cazul finit au fost resolvate problemele lui. A fost descris\u0103 structura quasigrupurilor finite simple paramediale (V.\u015ecerbacov);<\/li>\n<\/ul>\n<h4>Logic\u0103 matematic\u0103<\/h4>\n<ul>\n<li>Baza cercet\u0103rilor \u00een domeniul logicii matematice \u00een Institutul de Matematic\u0103 \u015fi Informatic\u0103 a fost pus\u0103 \u00een anul 1962 de c\u0103tre dr. Alexandr Kuznetov (1928-1984). Direc\u0163ia principal\u0103 de investiga\u0163ie o constituie abordarea problemelor de expresibilitate pentru calculele logice. \u00cen prezent cercet\u0103rile \u00een domeniul logicii matematice \u00een institut se efectueaz\u0103 sub conducerea membrului corespondent, profesorul M.Ra\u0163\u0103.<\/li>\n<li>a fost studiat\u0103 interpret\u0103rea opera\u0163iilor de baz\u0103 ale logicii demonstra\u0163ionale G\u00f6del-L\u00f6b pe algebrele lan\u0163iale. A fost determinat\u0103 o aplica\u0163ie a mul\u0163imii cuvintelor scrise \u00eentr-un alfabet finit \u00een mul\u0163imea formulelor unare a logicii demonstra\u0163ionale astfel realiz\u00e2ndu-se codificarea cuvintelor prin formule ale logicii demonstra\u0163ionale. (O. Izba\u015f);<\/li>\n<li>a fost construit\u0103 mul\u0163imea de clase \u00eenchise modelar-accesibile \u00een extensia 3-valent\u0103 a logicii demonstra\u0163ional-intui\u0163ioniste (O. Izba\u015f);<\/li>\n<li>a fost solu\u0163ionat\u0103 problema completitudinii functionale pentru logica propozitional\u0103 intui\u0163ionist\u0103 (M.Ra\u0163\u0103);<\/li>\n<li>a fost ob\u0163inut\u0103 solu\u0163ia pentru problema analogic\u0103 \u00een logica predicatelor de ordinul \u00eent\u00e2i (A.Kuznetov, M.Rata);<\/li>\n<li>a fost stabilit criteriul de expresibilitate parametric\u0103 pentru logica k-valent\u0103 (k=2, 3, _) (A.Kuznetov);<\/li>\n<li>au fost descoperite fenomene noi \u00een logica modala S4, cum ar fi existen\u0163a unei mul\u0163imi numerabile de clase pre-complete de formule, existen\u0163a bazelor de formule de orice lungime finit\u0103 \u015fi absen\u0163a aproxim\u0103rii finite \u00een raport cu completitudinea func\u0163ional\u0103 (M.Ra\u0163\u0103);<\/li>\n<li>a fost demonstrat\u0103 imposibilitatea construirii unui algoritm care ar solu\u0163iona problema de expresibilitate pentru logica modal\u0103 S4. Recent a fost demonstrat c\u0103 problema expresibilit\u0103\u0163ii pentru logica demonstra\u0163ional\u0103 Godel-Lob este algoritmic indecidabil\u0103 (M.Ra\u0163\u0103);<\/li>\n<li>au fost descrise opt serii de sisteme \u00eenchise \u00een lan\u0163 de func\u0163ii pseudo-booleene 3-valente (M.Ra\u0163\u0103).<\/li>\n<li>au fost stabilite condi\u0163iile necesare \u015fi suficiente de completitudine (func\u0163ional\u0103) a sistemelor de formule \u00een extensiile lan\u0163iale ale logicii dual intui\u0163ioniste. A fost construit\u0103 o algebr\u0103 iterativ\u0103 maximal\u0103 de func\u0163ii ale algebrei booleene topologice de ordinul 16 cu un atom deschis (M.Ra\u0163\u0103);<\/li>\n<li>\u00een logica demonstra\u0163ional-intui\u0163ionist\u0103 a fost construit\u0103 o mul\u0163ime num\u0103rabil\u0103 de clase modelar pre-complete. S-a demonstrat c\u0103 logica demonstra\u0163ional-intui\u0163ionist\u0103 nu este finit-aproximabil\u0103 relativ la completitudinea modelar\u0103 (O. Izba\u015f);<\/li>\n<\/ul>\n<h4>Algebr\u0103 topologic\u0103<\/h4>\n<p>Cercet\u0103rile \u00een domeniul algebrei topologice \u00een laborator se efectueaz\u0103 sub conducerea academicianului, profesorul V. Arnautov.<\/p>\n<ul>\n<li>\u00cen laticea tuturor topologiilor grupale pe un grup num\u0103rabil s-a ar\u0103tat c\u0103 este un continuum de coatomi \u015fi un continuum de topologii \u00een care grupul topologic are o baz\u0103 num\u0103rabil\u0103 de vecin\u0103t\u0103\u0163i ale unit\u0103\u0163ii \u015fi pentru orice dou\u0103 topologii \u03c41, \u03c42 , sup{\u03c41, \u03c42} este topologia discret\u0103. (V. Arnautov);<\/li>\n<li>Au fost descrise grupurile abeliene local compacte periodice cu proprietatea c\u0103 inelele de endomorfisme continui ale lor, echipate cu topologia compact-deschis\u0103, au cel mult dou\u0103 ideale \u00eenchise netriviale. (V. Popa) De asemenea, au fost caracterizate unele tipuri de grupuri abeliene local compacte cu proprietatea c\u0103 inelele de endomorfisme continui ale lor sunt inele Zorn. (V. Popa, S. Cruglea) \u00cen plus, au mai fost ob\u0163inute unele condi\u0163ii necesare pentru ca un grup abelian local compact s\u0103 fie + &#8211; complementat, respectiv, \u2229 &#8211; complementat. (V. Popa, Iu. Jardan);<\/li>\n<li>A fost elaborat\u0103 o metod\u0103 suficient de general\u0103 de a construi pe grupuri abeliene cu lan\u0163uri finite maximale cu extremit\u0103\u0163i fixate de topologii grupale. Pentru grupurile \u015fi inelele nilpotente au fost studiate propriet\u0103\u0163ile lan\u0163urilor necondensabile \u00een laticele principale de topologii de grup \u015fi topologii de inel, respectiv (V. Arnautov);<\/li>\n<li>Au fost ob\u0163inute estim\u0103rile num\u0103rului de extinderi unipunctale al topologiei definit\u0103 pe o mul\u0163ime finit\u0103. (V. Arnautov);<\/li>\n<li>A fost studiat\u0103 clasa inelelor ereditar liniar compacte. Au fost clasificate inelele semiprimitive ereditar liniar compacte, demonstrat\u0103 multiplicitatea acestei clase (analogul teoremei lui Tihonov) si a fost demonstrat\u0103 nilpoten\u0163a transfinit\u0103 a radicalului Jacobson al inelului. (M. Ursul)<\/li>\n<li>S-a demonstrat ca orice inel topologic se scufund\u0103 \u00eentr-un inel topologic liniar conex. Acest rezultat are o importan\u0163\u0103 remarcabil\u0103 \u00een teoria algebrelor topologice libere. (M. Ursul)<\/li>\n<li>S-a demonstrat ca orice inel compact nil are nilindice finit: in inele compacte toti radicalii nil coincid. Acest rezultat (coinciden\u0163a radicalilor nil) a fost extins la clasa inelelor liniar compacte. Inelele compacte nu indeplinesc nici o conditie clasica de finititudine.(M. Ursul)<\/li>\n<li>S-a demonstrat ca orice grup topologic Abelian se realizeaz\u0103 \u00een calitate de cvasicomponent\u0103 iterat\u0103 al unui alt grup topologic Abelian (problem\u0103 enuntat\u0103 de A. D.Taimanov). (M. Ursul)<\/li>\n<li>S-au construit exemple de corpuri topologice compacte de orice dimensiune finit\u0103 Menger-Urysohn (problema existen\u0163ei unor astfel de corpuri a fost formulat\u0103 de E. Vecitomov, V.Belinov, D.Shakhmatov, W.Comfort). (M. Ursul)<\/li>\n<li>Au fost descrise, \u00een termeni de extinderi ideale de inele topologice, inelele topologice av\u00e2nd cel mult dou\u0103 ideale \u00eenchise netriviale. (V. Popa);<\/li>\n<li>Pentru diferite clase de grupuri abeliene local compacte au fost descrise grupurile din aceste clase cu proprietatea c\u0103 inelele de endomorfisme continue ale lor, considerate cu topologia compact-deschis\u0103, verific\u0103 una dintre urm\u0103toarele condi\u0163ii:\n<ul>\n<li>constau din elemente topologic idempotente;<\/li>\n<li>nu con\u0163in elemente nilpotente nenule;<\/li>\n<li>sunt inele Zorn;<\/li>\n<li>sunt dens divizibile \u015fi f\u0103r\u0103 torsiune care sunt + &#8211; complementate, respectiv, &#8211; complementate;<\/li>\n<li>sunt topologic simple;<\/li>\n<li>componenta de conexitate a lor este respectiv m\u0103rginit\u0103, local compact\u0103, sau compact\u0103;<\/li>\n<li>sunt compacte;<\/li>\n<li>sunt comutative. (V. Popa).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h4>Geometria grupurilor discrete<\/h4>\n<p>Direc\u0163ia de baz\u0103 \u00een cercet\u0103rile promovate \u00een geometrie \u00een laborator o constituie studiul grupurilor discrete, al variet\u0103\u0163ilor \u015fi descompunerilor spa\u0163iilor de curbur\u0103 constant\u0103.<\/p>\n<ul>\n<li>au fost determinate descompunerile 3-izoedrice ale sferei pentru unele serii infinite de grupuri de izometrii. (E. Zamorzaeva);<\/li>\n<li>au fost obtinute poliedre fundamentale cu volumuri egale pentru diferite grupuri discrete de miscari ale spatiului hiperbolic. (I. Gutul);<\/li>\n<li>au fost construite noi serii de poliedre compacte \u015fi necompacte de volum finit ce descompun regular normal \u015fi regular anormal spa\u0163iile hiperbolice cu dimensiunile n = 3, 4, 5 (I. Gu\u0163ul, V. Macarov);<\/li>\n<li>au fost construite serii de variet\u0103\u0163i hiperbolice compacte \u015fi necompacte de volum finit at\u00e2t orientate, c\u00e2t \u015fi neorientate \u00een dimensiunile 3, 4 \u015fi 5. Au fost studiate subvariet\u0103\u0163ile scufundate total geodezic de codimensiunea 1 \u015fi au fost realizate noi exemple de variet\u0103\u0163i prin reconstruc\u0163ii metrice, ce corespund HNN extensiunilor grupului fundamental (F. Damian, I. Gu\u0163ul, V. Macarov);<\/li>\n<li>au fost elaboprate metode de ob\u0163inere a tuturor descompunerilor k-izoedrice pentru spa\u0163ii bidimensionale de curbur\u0103 constant\u0103. Cu ajutorul acestor metode au fost efectuate clasific\u0103rile parti\u0163iilor 2-izoedrice pentru planul euclidian \u015fi sfer\u0103. Au fost cercetate unele aspecte ale acestor metode pentru spa\u0163iu (E. Zamorzaeva);<\/li>\n<li>Au fost construite variet\u0103\u0163i hiperbolice de dimensiune 4 cu diferite caracteristici Euler \u015fi studiat\u0103 geometria lor.<\/li>\n<li>Au fost ob\u0163ine poliedre tri-dimensionale prin metoda metric\u0103 (I. Gu\u0163ul);<\/li>\n<li>Descompunerile monoedrice \u015fi cunoscutele descompuneri diedrice au fost analizate sub aspectul claselor de trantitivitate ale celulelor (E. Zamorzaeva);<\/li>\n<li>A fost cercetat\u0103 geometria interioar\u0103 a cusp-urilor pentru variet\u0103\u0163i hiperbolice de diferit\u0103 dimensiune. Au fost analizate metode de ob\u0163iere a variet\u0103\u0163ilor cu cusp-uri peste forme spa\u0163ile concrete (F. Damian);<\/li>\n<\/ul>\n<h3>Lucr\u0103ri de referin\u0163\u0103<\/h3>\n<h4>Monografii \u015fi c\u0103r\u0163i<\/h4>\n<ol>\n<li>Belyavskaya G. \u041a\u0432\u0430\u0437\u0438\u0433\u0440\u0443\u043f\u043f\u044b: \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0430 \u0441 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430\u043c\u0438, \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0441\u0442\u044c \u0438 \u044f\u0434\u0440\u0430. LAP Lambert Academic Publishing. 2013. \u0441\u0442\u0440. 80.<\/li>\n<li>\u0410\u0440\u043d\u0430\u0443\u0442\u043e\u0432 \u0412. \u0418., \u0415\u0440\u043c\u0430\u043a\u043e\u0432\u0430 \u0413. \u041d. \u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0442\u0435\u043e\u0440\u0438\u044e \u0442\u043e\u043f\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0433\u0440\u0443\u043f\u043f. \u041a\u0438\u0448\u0438\u043d\u0435\u0432. Universitatea de Stat din Tiraspol. 2013.- 215 p.<\/li>\n<li>M. Ra\u0163iu, Algebre iterative lan\u0163iale de func\u0163ii pseudo-booleene trivalente, Ia\u015fi: Editura Alexandru Myller, 2010, 276 p.<\/li>\n<li>\u0412. \u0410\u0440\u043d\u0430\u0443\u0442\u043e\u0432, \u041d. \u041c\u0430\u043b\u044e\u0442\u0438\u043d\u0430, \u041e\u0431\u0449\u0430\u044f \u0442\u043e\u043f\u043e\u043b\u043e\u0433\u0438\u044f. Textbooks and Monographs, Moldova State University, Center for Education and Research in Mathematics and Computer Science (CERIM-1006.06, MRDA\/CRDF) Ch.: CEP USM, 2010, 108 p.<\/li>\n<li>\u0412. \u0410\u0440\u043d\u0430\u0443\u0442\u043e\u0432, \u0413. \u0415\u0440\u043c\u0430\u043a\u043e\u0432\u0430, \u041a\u0430\u0440\u0434\u0438\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0442\u0440\u0430\u043d\u0441\u0444\u0438\u043d\u0438\u0442\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430. \u0421\u0435\u0440\u0438\u044f \u0443\u0447\u0435\u0431\u043d\u0438\u043a\u0438 \u0438 \u043c\u043e\u043d\u043e\u0433\u0440\u0430\u0444\u0438\u0438, \u0422\u043e\u043c 9, Universitatea de Stat din Moldova Centrul de educa\u0163ie \u015fi Cercetare \u00een Matematic\u0103 \u015fi Informatic\u0103 al USM (CECMI USM) &#8211; Ch.: CEP USM, 2010, 76p.<\/li>\n<li>A. Ca\u015fu, I. Goian, P. S\u00e2rbu, Sisteme numerice, Centrul Editorial al USM, Chi\u015fin\u0103u, 2008.<\/li>\n<li>M. Ra\u0163\u0103, Inexisten\u0163a algoritmilor de recunoa\u015ftere a expresibilit\u0103\u0163ii sintactice \u00een calcule logice, Pite\u015fti, Rom\u00e2nia, The Flower power. 2004.<\/li>\n<li>\u0412. \u0410\u043d\u0434\u0440\u0443\u043d\u0430\u043a\u0438\u0435\u0432\u0438\u0447, \u042e. \u0420\u044f\u0431\u0443\u0445\u0438\u043d. \u0420\u0430\u0434\u0438\u043a\u0430\u043b\u044b \u0430\u043b\u0433\u0435\u0431\u0440 \u0438 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0438\u044f, \u041c\u043e\u0441\u043a\u0432\u0430, \u041d\u0430\u0443\u043a\u0430, 1973.<\/li>\n<li>V. Arnautov, S. Glavatky, A. Mikhalev, Introduction to the theory of topological rings and modules, Marcel Dekker, Inc., New York &#8211; Basel &#8211; Hong Kong, 1996.<\/li>\n<li>V. Arnautov, The theory of radicals of topological rings, Mathematica Japonica, 1998, Vol. 47, No.3, p. 439 \u2013 544.<\/li>\n<li>\u0412. \u0411\u0435\u043b\u043e\u0443\u0441\u043e\u0432, \u041e\u0441\u043d\u043e\u0432\u044b \u0442\u0435\u043e\u0440\u0438\u0438 \u043a\u0432\u0430\u0437\u0438\u0433\u0440\u0443\u043f\u043f \u0438 \u043b\u0443\u043f, \u041c\u043e\u0441\u043a\u0432\u0430, \u041d\u0430\u0443\u043a\u0430, 1967.<\/li>\n<li>\u0412. \u0411\u0435\u043b\u043e\u0443\u0441\u043e\u0432, \u0410\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0435\u0442\u0438 \u0438 \u043a\u0432\u0430\u0437\u0438\u0433\u0440\u0443\u043f\u043f\u044b, \u041a\u0438\u0448\u0438\u043d\u0451\u0432, \u0428\u0442\u0438\u0438\u043d\u0446\u0430, 1971.<\/li>\n<li>\u0412. \u0411\u0435\u043b\u043e\u0443\u0441\u043e\u0432, \u041a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438 \u0432 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u0435\u0442\u044f\u0445, \u041a\u0438\u0448\u0438\u043d\u0451\u0432, \u0428\u0442\u0438\u0438\u043d\u0446\u0430, 1979.<\/li>\n<li>G.B. Belyavskaya, r-Orthogonal latin squares. Chapter 6 in the collection \u201cLatin squares: New Developments in the Theory and Applications\u201d. Annals of Discrete Mathematics, V.46, 1991, North-Holland-Amsterdam-New-York \u2013Oxford-Tokyo, p.169-202.<\/li>\n<li>A. Ca\u015fu, Introducere \u00een teoria modulelor, Centrul Editorial al USM, Chi\u015fin\u0103u, 2003.<\/li>\n<li>A. \u041a\u0430\u0448\u0443, \u0420\u0430\u0434\u0438\u043a\u0430\u043b\u044b \u0438 \u043a\u0440\u0443\u0447\u0435\u043d\u0438\u044f \u0432 \u043c\u043e\u0434\u0443\u043b\u044f\u0445, \u041a\u0438\u0448\u0438\u043d\u0451\u0432, \u0428\u0442\u0438\u0438\u043d\u0446\u0430, 1983.<\/li>\n<li>A. \u041a\u0430\u0448\u0443, \u0424\u0443\u043d\u043a\u0442\u043e\u0440\u044b \u0438 \u043a\u0440\u0443\u0447\u0435\u043d\u0438\u044f \u0432 \u043a\u0430\u0442\u0435\u0433\u043e\u0440\u0438\u044f\u0445 \u043c\u043e\u0434\u0443\u043b\u0435\u0439, \u041a\u0438\u0448\u0438\u043d\u0451\u0432, \u0410\u043a\u0430\u0434\u0435\u043c\u0438\u044f \u041d\u0430\u0443\u043a \u0420\u041c, \u0418\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438, 1997.<\/li>\n<li>M. \u0420\u0430\u0446\u0430, \u0418\u0442\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u044b\u0435 \u0446\u0435\u043f\u043d\u044b\u0435 \u043a\u043b\u0430\u0441\u0441\u044b \u043f\u0441\u0435\u0432\u0434\u043e\u0431\u0443\u043b\u0435\u0432\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u041a\u0438\u0448\u0438\u043d\u0451\u0432, \u0428\u0442\u0438\u0438\u043d\u0446\u0430, 1990.<\/li>\n<li>M. \u0420\u0430\u0446\u0430, \u0412\u044b\u0440\u0430\u0437\u0438\u043c\u043e\u0441\u0442\u044c \u0432 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f\u0445 \u0432\u044b\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u043d\u0438\u0439, \u041a\u0438\u0448\u0438\u043d\u0451\u0432, \u0428\u0442\u0438\u0438\u043d\u0446\u0430, 1991.<\/li>\n<li>\u041c. \u0423\u0440\u0441\u0443\u043b, \u041a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u044b\u0435 \u043a\u043e\u043b\u044c\u0446\u0430 \u0438 \u0438\u0445 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u044f, \u041a\u0438\u0448\u0438\u043d\u0451\u0432, \u0428\u0442\u0438\u0438\u043d\u0446\u0430, 1991.<\/li>\n<\/ol>\n<h4>Articole<\/h4>\n<ol>\n<li>Kashu A. I. Closure operators in the categories of modules. Part I ( Weakly hereditary and idempotent operators ). Algebra and Discrete Mathematics, vol.15 (2013), \u2116 2, pp.213-228. Part II Algebra and Discrete Mathematics, vol.16 (2013), \u2116 1, pp.81-95.<\/li>\n<li>Izbash V. Commuting polinomials in the medial quasigroups. Proceedings of The 37th Anual Congress of the American Romanian Academy of Arts and Sciences (ARA). The university of Euopean Political and Economic Studies &#8220;Constantin Stere&#8221;, June 04-09, 2013: Presses internationales Polytechnique, Montreal, Quebec, Canada, Proceedings. &#8211; Chi\u015fin\u0103u. 2013, pp. 463-466.<\/li>\n<li>Izbash O. Applying of predicates for settlement of model completeness in the 3-valued extension of provability-intuitionistic logic. Proceedings of The 37th Anual Congress of the American Romanian Academy of Arts and Sciences (ARA). The university of Euopean Political and Economic Studies &#8220;Constantin Stere&#8221;, June 04-09, 2013: Presses internationales Polytechnique, Montreal, Quebec, Canada, Proceedings.-Chi\u015fin\u0103u. 2013, pp. 467-470.<\/li>\n<li>Berezin A. N., Moldovyan N. A., Scerbacov V. A. Cryptoschemes Based on Difficulty of Simultaneous Solving Two Different Difficult Problems, CSJM v.21, n.2 (62) (2013) 280-290.<\/li>\n<li>Arnautov V.I.; Ermakova G.N. On the number of group topologies on countable groups. Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova. Matematica, \u2116 2 (72), 2013, p. 3-12<\/li>\n<li>Drapal A., Shcherbacov V. A. Identities and the group of isostrophisms. Comment. Math. Univ. Carolin. 2012, 53(3), 347-374.<\/li>\n<li>Arnautov V. I. Tmethod of construction of topologies on any finite set. Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2012, \u2116 2 ( 69 ).<\/li>\n<li>Belyavskaya G. Recursively r-differentiable quasigroups within S-systems and MDS-codes. Quasigroups and Related Systems, vol. 20, no. 2, 2012.<\/li>\n<li>Zamorzaeva E. A. Isohedral on Riemann surfaces of genus 2. Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2012, \u2116 2 ( 69 ).<\/li>\n<li>Ra\u0163iu M. Method of the formula realization of algebras and its application in mathematical logic. Proceedings of The 36th Anual Congress of the American Romanian Academy of Arts and Sciences (ARA). Learing Without Frontiers. Giola del Colle &#8211; Bari, Italia, May 30th &#8211; June 2nd, 2012. Presses internationales Polytechnique, Montreal, Quebec, Canada, 2012, pp. 137-140.<\/li>\n<li>Kuznetsov E. Transversals in loops.2.Structural theorems. Quasigroups and related systems, 2011, 19, No. 2 , 279-286.<\/li>\n<li>Popa V. On LCA groups whose rings of continuous endomorphisms have at most two non-trivial closed ideals. I, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2011, nr. 3(67), 91-107.<\/li>\n<li>V. Arnautov, Estimation of the number of one-point expansion of a topology is given on a finite set. Buletinul A.\u015e.R.M. Matematica, 2011, nr. 2(66), p. 17-22, ISSN 1024-7696.<\/li>\n<li>A. Kashu, On some operations in the lattice of submodules determined by preradicals. Buletinul A.\u015e.R.M. Matematica, 2011, nr. 2 (64), p. 5\u201316.<\/li>\n<li>G. B. Belyavskaya, V. I. Izbash, A. Moldovyan, V. A. Shcherbacov, Digital signature and secret-sharing schemes. Conf. &#8220;Cercetarea \u015fi inovarea \u043en parteneriat cu mediul de afaceri&#8221;, Chi\u015fin\u0103u, XI, 2011.<\/li>\n<li>G. B. Belyavskaya, T. Popovich, \u0422\u043e\u0442\u0430\u043b\u044c\u043d\u043e \u043f\u0430\u0440\u0430\u0441\u0442\u0440\u043e\u0444\u043d\u043e \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u043a\u0432\u0430\u0437\u0438\u0433\u0440\u0443\u043f\u043f\u044b \u0438 \u043f\u043e\u043b\u043d\u044b\u0435 \u0433\u0440\u0430\u0444\u044b. \u0424\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0438 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u0430\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u041c\u043e\u0441\u043a\u0432\u0430, 2010.<\/li>\n<li>O. Izba\u015f, O serie infinit\u0103 de clase modelar pre-complete \u00een logica demonstra\u0163ional intui\u0163ionist\u0103. In: The 34th Annual Congress, American Ramanian Academy of Arts and Sciences (ARA), May 18th-23rd, Bucharest, Ramania, 2010, Proceedings. Sci. Ed.: Frunzeti T., Hanganu M. \u2013 Presses Internationales Polytechnique, Montr\u00e9al, Qu\u00e9bec, 2010, p. 571-574.<\/li>\n<li>A. Kashu, Preradicals and characteristic submodules: connections and operations. Algebra and discrete mathematics, 2010, vol. 9, nr. 2, p. 59-75.<\/li>\n<li>V. A. Shcherbacov, D. I. Pushkashu, On the structure of finite paramedial quasigroups. Comment. Math. Univ. Carolin, 2010, 51(2), p. 357-370.<\/li>\n<li>V. Shcherbacov, On the structure of left and right F-, SM-, and E-quasigroups. \u00cen: Journal of Generalized Lie Theory and Applications, 2009, vol. 3, No. 3, p. 197&#8211;259.<\/li>\n<li>\u042e. \u041c. \u0420\u044f\u0431\u0443\u0445\u0438\u043d, \u0421\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0438\u044f \u0438 \u0442\u0435\u043e\u0440\u0438\u044f \u0440\u0430\u0434\u0438\u043a\u0430\u043b\u043e\u0432 \u2013 \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f. \u0412 \u043a\u043d\u0438\u0433\u0435: &#8220;Academicianul Vladimir Andrunachievici&#8221;, A\u015eM, IMI, Chi\u015fin\u0103u, 2009, p. 149 \u2013 177.<\/li>\n<li>M. Ra\u0163\u0103, Algebre iterative lan\u0163iale de func\u0163ii pseudo-booleene 3-valente. In: Proceedings of the 33rd Annual Congress of the American Romanian Academy of Arts and Sciences (ARA), 2009, Vol. 2, Polytechnic International Press, Montreal, Quebec, p. 321-323<\/li>\n<li>V. Shcherbacov, On the structure of left and right F-, SM-, and E-quasigroups. \u00cen: Journal of Generalized Lie Theory and Applications, 2009, Vol. 3, No. 3, p. 197&#8211;259.<\/li>\n<li>V. I. Arnautov, About group topologies of the primary Abelian groups of finite period, which coincide on a subgroup and on a factor group. In: Buletinul A.\u015e.M., Matematica, 2009, No.2 (60), p.12-28.<\/li>\n<li>A.I., Kashu, On preradicals associated to principal functors of module categories , I . In: Buletinul A.\u015e.M., Matematica, 2009, \u2116 2 ( 60 ), p. 62 \u2013 72 .<\/li>\n<li>G.B. Belyavskaya, \u0410\u0441\u0441\u043e\u0446\u0438\u0430\u043d\u0442\u044b \u0438 \u043a\u043e\u043c\u043c\u0443\u0442\u0430\u043d\u0442 \u043a\u0432\u0430\u0437\u0438\u0433\u0440\u0443\u043f\u043f\u044b. \u0424\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f. \u0438 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u0430\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u041c\u043e\u0441\u043a\u0432\u0430, 1997, \u0442.3, \u0432\u044b\u043f.3, \u0441. 715-737.<\/li>\n<li>G.B. Belyavskaya, Associators, commutators and linearity of a quasigroup. Discrete mathematics and Applications, 1996, v.5, \u21166, p.577-586.<\/li>\n<li>G.B. Belyavskaya, V.I. Izbash, G.L. Mullen , Check character systems using quasigroups:I. Designs, Codes and Cryptography, 37, 2005, pp. 215-227.<\/li>\n<li>G.B. Belyavskaya, Gary L. Mullen, Strongly orthogonal and uniformly orthogonal many-placed operations. Algebra and Discrete , Mathematics , Ukraine, N1, 2006, p. 1-17.<\/li>\n<li>Izbash V., Syrbu P. On recursively differentiable binary quasigroups. Proceedings of 11-th Conf. on Applied and Industrial Mathematics. Romania, Oradea, CAIM 2003, v. 1, pp. 149-152.<\/li>\n<li>Baltag V., Izba\u015f V. Olimpiade matematice. Ministerul educa\u0163iei Al Republicii Moldova, Consiliul olimpic de matematic\u0103, Institutul de matematic\u0103 \u015fi Informatic\u0103 al A\u015eM, Chi\u015fin\u0103u 2003<\/li>\n<li>Izbash V., Syrbu P. Recursively differentiable quasigroups and complete recursive codes. Comment. Math. Univ. Carolinae 45, 2 (2004) 257-263.<\/li>\n<li>Izbash V. On automorphisms of the Cartesian square of a groupoid. Quasigroups and Related Systems 5(1998), 99-106.<\/li>\n<li>Izbash V., Labo N. Crossed-inverse-property groupoids, Buletinul ASM. Matematica. Number 2(54), 2007, Pages 101-106.<\/li>\n<li>E. Kuznetsov. A loop transversal in a sharply 2-transitive permutation loop. Bulletin of the Acad. of Sci. of Moldova, Mathematics, #3(49), 2005, p. 101-114.<\/li>\n<li>E. Kuznetsov. Gyrogroups and left gyrogroups as transversals of a special kind. Algebra and Discrete Math., #3, 2003, p. 54-81.<\/li>\n<li>E. Kuznetsov. Transversals in groups. 4. Derivation construction. Quasigroups and related systems, 9(2002), p. 67-84.<\/li>\n<li>E. Kuznetsov. Incidence systems over groups that can be supplemented up to projective planes. Quasigroups and related systems, 5(1998), p. 35-52.<\/li>\n<li>E. Kuznetsov. About some algebraic systems related with projective planes. Quasigroups and related systems, 2(1995), \u21161, p. 6-33.<\/li>\n<li>V. Shcherbacov, V. Izbash. On quasigroups with Moufang identity. Buletinul AS RM. Matematica. No 2, 1998, p. 109-116.<\/li>\n<li>G. L. Mullen, V.A. Shcherbacov, Properties of codes with one check symbol from a quasigroup point of view, Izvestiya AN RM. Matematica. No 3, 2002, p. 71-86.<\/li>\n<li>A.D. Keedwell, V.A. Shcherbacov, Construction and properties of (r,s,t)-inverse quasigroups. I, Discrete Math., V. 266, No. 1-3, 2003, p. 275-291.<\/li>\n<li>V. A. Shcherbacov, On simple n-ary medial quasigroups, Proceedings of Conference &#8220;Computational Commutative and Non-Commutative Algebraic Geometry&#8221;, NATO Science Series: Computer and Systems Sciences, Edited by S. Cojocaru, G. Pfister and V. Ufnarovski, IOS Press, V. 196, 2005, p. 305&#8211;324.<\/li>\n<li>G.L. Mullen, V.A. Shcherbacov, On orthogonality of binary operations and squares, Buletinul A\u015e RM. Matematica. No 2(48), 2005, p. 3-42.<\/li>\n<li>V. A. Shcherbacov, On Bruck-Belousov problem, Buletinul A\u015e RM. Matematica. No 3(49), 2005, p. 123-140.<\/li>\n<li>V.A. Shcherbacov, On the structure of left and right F-, SM- and E-quasigroups, arXiv:0811.1725, 67 pages.<\/li>\n<li>V. Arnautov, K. Filippov, On disjoint sums in the lattice of linear topologies, \u0424\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0438 \u041f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u0430\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0442. 9, No 1, \u0441. 3-18, \u041c\u043e\u0441\u043a\u0432\u0430, 2003.<\/li>\n<li>V. Arnautov, On overnilpotent radicals of topological rings, Buletinul Academiei de \u015etiin\u0163ei a Republicii Moldova, Matematica, v. 1(44), 2004, p. 3 &#8212; 14.<\/li>\n<li>V. Arnautov, Properties of one-sided ideals of topological rings, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2006, v. 1(50), p.3-14.<\/li>\n<li>V. Arnautov, \u041e \u043d\u0430\u043a\u0440\u044b\u0442\u0438\u044f\u0445 \u0432 \u0440\u0435\u0448\u0435\u0442\u043a\u0435 \u0432\u0441\u0435\u0445 \u0433\u0440\u0443\u043f\u043f\u043e\u0432\u044b\u0445 \u0442\u043e\u043f\u043e\u043b\u043e\u0433\u0438\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u043e\u0439 \u0430\u0431\u0435\u043b\u0435\u0432\u043e\u0439 \u0433\u0440\u0443\u043f\u043f\u0435, \u0421\u0438\u0431. \u041c\u0430\u0442. \u0416\u0443\u0440\u043d., 2006, \u0442.47, \u2116 5, 961-973.<\/li>\n<li>V.Arnautov, Quotient rings of pseudonormed rings, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2006, v. 2(51), p.3-16.<\/li>\n<li>V. Arnautov, Properties of accessible subrings of topological rings when taking quotien rings, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2007, v. 2(54), p.4-18.<\/li>\n<li>A. Kashu, On equivalence of some subcategories of modules in Morita contexts. Algebra and Discrete Mathematics. N 3, 2003, p. 46 \u2013 53.<\/li>\n<li>A. Kashu, On natural classes of R-modules, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2004, v. 2(45), p.95-101.<\/li>\n<li>A. Ca\u015fu, Natural classes and torsion free classes in categories of modules, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2006, v. 3(52), p.45-50.<\/li>\n<li>A. Ca\u015fu, On natural and conatural sets of left ideals of a ring, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2007, v. 2(54), p.25-32.<\/li>\n<li>V. Popa, On endomorphism rings without nonzero nilpotent elements. I, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 1998, 3(28), 35-48.<\/li>\n<li>V. Popa, On endomorphism rings without nonzero nilpotent elements. II, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 1999, 2(30), 91-104.<\/li>\n<li>V. Popa, On the connected component of a homomorphism group, Mathematica, Editions de l\u2019Academie Roumaine, Cluj-Napoca, 1999, Tome 41(64), nr. 1, 69-83.<\/li>\n<li>V. Popa, On LCA groups with compact rings of continuous endomorphisms, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2000, 1(32), 17-32.<\/li>\n<li>V. Popa, On topological torsion LCA groups with commutative ring of continuous endomorphisms, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2006, v. 3(52), p.29-42.<\/li>\n<li>V. Popa, On LCA groups in which some closed subgroups have commutative rings of continuous endomorphisms, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2007, v. 1(53), p.83-94.<\/li>\n<li>V. Popa, On torsionfree LCA groups with commutative rings of continuous endomorphisms, Buletinul Academiei de \u015etiin\u0163e a Republicii Moldova, Matematica, 2007, v. 2(54), p.81-100.<\/li>\n<li>B.Afanasov, I.Gutul. Suprafe\u0163e total geodezice cu simetrie bogat\u0103 \u015fi 3-variet\u0103\u0163i \u00eenchise cu poliedru fundamental comun. Topology&#8217;90, Walter de Gruyter, Berlin-New York, 1991, p.37-53 (\u00een limba englez\u0103).<\/li>\n<li>O.Delgado, D.Huson, E.Zamorzaeva, Clasificarea descompunerilor 2-izoedrice ale planului. Geometriae Dedicata, vol.42, no.1, 1992, p.43-117 (in limba engleza).<\/li>\n<li>\u0418. \u0413\u0443\u0446\u0443\u043b, \u041e \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0447\u0435\u0442\u044b\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u044b\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043c\u043d\u043e\u0433\u043e\u043e\u0431\u0440\u0430\u0437\u0438\u044f\u0445, International Seminar on Discrete Geometry dedicated to the 75 birth day of professor A.M. Zamorzaev, Chi\u015fin\u0103u, 2002, p. 35-40.<\/li>\n<li>I. Gu\u0163ul, Some hyperbolic manifolds, Buletinul de \u015etiin\u0163e a Republicii Moldova, Matematica, 2004, \u21163, p. 63-71.<\/li>\n<li>M. Ursul, Locally finite and locally projectively nilpotent ideals in topological rings, Matematiceskii Sbornik (N.S.) 125(167) (1984), p. 291-305<\/li>\n<li>M. Ursul, Compact nilrings, Matematiceskie Zametki, 36(6) (1984), p.839-845<\/li>\n<li>M. Ursul, On product of hereditarily lineary compact rings, Uspehi Matematiceskih Nauk, 36(3) (1980), p. 230-233<\/li>\n<li>M. Ursul, I. Florea, F-quasigroups with the property of invertibility (IPF-quasigroups), Voprosy Teorii Kvasigrupp i Lup. Kishinev. RIO AN MSSR, 1970, p. 145-146<\/li>\n<\/ol>\n<\/div>\n<div id=\"right\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Direc\u0163ii de cercetare Algebra (teoria radicalilor, probleme de structura \u00een sisteme algebrice apropiate inelelor, modulelor \u015fi algebrelor); Quasigrupuri \u015fi analiza combinatorie (teoria general\u0103 a quasigrupurilor \u015fi opera\u0163iilor algebrice, probleme de combinatoric\u0103 \u00een quasigrupuri \u015fi aplica\u0163ii la codificarea \u015fi cifrarea informa\u0163iei); Logica matematic\u0103 (probleme algoritmice ale expresibilit\u0103\u0163ii func\u0163ionale precum \u015fi ale generaliz\u0103rilor ei \u00een logici neclasice); [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-48","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/pages\/48","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=48"}],"version-history":[{"count":3,"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/pages\/48\/revisions"}],"predecessor-version":[{"id":138,"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=\/wp\/v2\/pages\/48\/revisions\/138"}],"wp:attachment":[{"href":"https:\/\/idcmi.usm.md\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}