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Information × Registration Number 0224U000877, 0124U000142 , R & D reports Title Construction of new models of some free algebras of small ranks and endomorphism semigroups popup.stage_title Head Zhuchok Anatolii V., Доктор фізико-математичних наук Registration Date 14-01-2024 Organization State establishment "Luhansk Taras Shevchenko national University" popup.description2 CОNGRUENCE, SEMIGROUP, n-TUPLE SEMIGROUP, FREE n-TUPLE SEMIGROUP, DIGROUP, FREE MONOGENIC DIGROUP, GENERALIZED DIGROUP, DIMONOID, FREE ABELIAN DIMONOID OF RANK 2, DOPPELSEMIGROUP, ENDOMORPHISM SEMIGROUP, ENDOTOPISM SEMIGROUP, EQUIVALENCE. Objects of the research are n-tuple semigroups, free k-nilpotent n-tuple semigroups, free monogenic commutative doppelsemigroups, digroups, free monogenic digroups, free dimonoids, semigroups, binary relations. Subjects of the research are the structure of free k-nilpotent n-tuple semigroups, free monogenic commutative doppelsemigroups, free monogenic digroups, free dimonoids and endomorphism semigroups of equivalence relations. The objective: conducting fundamental researches in such theories as the theory of universal algebra, the theory of digroups and the modern theory of semigroups, and a publication of the results of these studies in professional scientific journals of Ukraine and / or international journals included in scientometric databases Scopus and / or Web of Science. Research results: k-nilpotent n-tuple semigroups are constructed; a review of the results from the theory of n-tuple semigroups is made; the new models for some free algebras of small ranks are constructed; a new class of digroups defined by arbitrary groups is constructed; a new model of a free monogenic digroup in terms of the group of integers is defined; B. I. Plotkin’s problem on the description of automorphisms of the category of free finitely generated algebras for a variety of free dimonoids is solved; a weak endomorphism semigroup of the strict partial equivalence relation is studied. Results сan be used during researches on this topic and included in programs of courses for students of mathematical specialties. Product Description popup.authors Zhuchok Anatolii V. Zhuchok Yuliia Volodymyrivna Zhuchok Yurii Volodymyrovych Toichkina Olena Oleksandrivna popup.nrat_date 2024-01-14 Close