Modern trends in algebra, topology and geometry: fundamental researches and applications

Programmee:Institutional Projects (Supreme Council for Science and Technological Development)
Execution period:2015 – 2019
Institutions:Institute of Mathematics and Computer Science
Project Leader:Kashu Alexei
Participants: Izbash Vladimir, Arnautov Vladimir, Shcherbacov Victor, Ryabukhin Yuri, Belyavskaya Galina, Popa Valeriu, Gutsul Ion, Damian Florin, Zamorzaeva Elizaveta, Kuznetsov Eugene, Izbash Olga, Cojuhari Elena, Botnari Serghei, Jardan Ion, Morarasu Ecaterina, Luchian Mihail, Cebanu Victor, Țărnă (Vieru) Tatiana, Cruglea Serafima


The objectives: the investigation and solution of some important problems of modern mathematics from algebra, topology and geometry; publication and popularization of obtained results; the specification of the ways of application of them in diverse domains.

The role and significance of the project consist in:

  1. the new achievements in researches of algebraic, topological and geometrical systems, connected by the actual problems of these domains;
  2. the support and progress of the existing in the country scientific schools, which have remarkable successes and traditions in algebra, topology and geometry; the implication of youth specialists in the scientific investigation;
  3. the search of real possibilities of implementation of some new results in different domains (science, education, economy).

The methods utilized in the investigations are both the classical methods of the mentioned domains of mathematics and the new aspects and points of view, related by some notions, constructions and modern trends: varieties and universal properties, the language and techniques of category theory, interdisciplinary researches.

The necessary conditions for successful realization of the project planned tasks are ensured by:

  1. the existence of fundamental results obtained in Moldova, which can serve as a stable base for continuation of investigations in the mentioned domains;
  2. the existence of a strong collective of specialists of high qualification, the laboratory „Algebra and topology” of IMCS of ASM, which continues the traditions and subjects of scientific schools founded by well-known mathematicians V. Andrunachievich and V. Belousov.

The expected results:

  1. Elucidation of properties of the lattices of congruences, of automorphism groups, of groups of isotopies, parastrophies of some classes of quasigroups and groupoids; the relations between the orthogonal systems of operations, which are applied in cryptology;
  2. Description of local compact abelian groups, for which ring of continued endomorphisms satisfies some finiteness conditions;
  3. Construction of some decompositions in polyhedrons by three independent metric parameters;
  4. Finding the criterion of functional completeness in the 16-valued extension of EM4 modal logic;
  5. Establishment of relations between the preradicals and closure operators of a module category.