The branch of the Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine (director – Zhuchok A. V., Doctor of Physical and Mathematical Sciences, Professor) was established in 2004 with the aim of organizing comprehensive research on the problems of mathematics and their applications.
The branch continued to carry out fundamental research in mathematics and its applications.
The research is devoted to the study of such algebraic systems as doppel semigroups, n-fold semigroups and trioids. He solved the problem of describing a free n-fold semigroup of arbitrary rank. He constructed some relatively free doppel semigroups, in particular, free abelian doppel semigroups. He presented the construction of a free commutative trioid. He solved the problem of characterizing groups of automorphisms constructed relative to free algebras. Described a series of smallest congruences on constructed free n-fold semigroups, trioids and doppelsemigroups.
The results of the work have theoretical significance as such, being a contribution to the further development of the theory of ordered doppelsemigroups and trioids.
Nine issues of the journal were published on the basis of the branch in 2019-2024 «Algebra and Discrete Mathematics».