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Information × Registration Number 0223U000565, 0123U100168 , R & D reports Title Axiomatic and relational properties of trioids and some semigroups of transformations popup.stage_title Head Zhuchok Anatolii V., Доктор фізико-математичних наук Registration Date 12-01-2023 Organization State establishment "Luhansk Taras Shevchenko national University" popup.description2  n-TRINILPOTENT TRIOID, FREE TRIOID, FREE ABELIAN TRIOID, FREE MONOGENIC TRIOID, DIMONOID, CONGRUENCE, ENDOMORPHISM SEMIGROUP, ENDOTOPISM SEMIGROUP, EQUIVALENCE. Objects of the research are n-trinilpotent trioids, free trioids, free dimonoids, semigroups, binary relations. Subjects of the research are the structure of n-trinilpotent trioids, free trioids, free dimonoids and endomorphism semigroups of these objects. The objective: conducting fundamental researches in such theories as the theory of dimonoids and the theory of trioids, the theory of semigroups, and a publication of 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: independence of axioms of a trioid is prove; the smallest dimonoid congruences and the smallest semigroup congruences on free left(right) n-trinilpotent trioids and free abelian trioids are characterized; the new model for the free commutative trioid of rank 1 is constructed; all endomorphisms of free commutative monogenic trioid are described; it is shown that the endomorphism semigroup of the free commutative monogenic trioid can be represented as the adjoint semigroup of some natural semiring defined on the trioid; the new model for the free generalized digroup of rank 1 is represented; a new model for the free abelian dimonoid of rank 2 is constructed; a new model for the free commutative dopelsemigroup of rank 1 is constructed; a new simpler model for the free digroup of rank 1 is defined; the necessary and sufficient conditions under which the endotopism semigroup of an equivalence relation is an ordered semigroup with respect to the given order are defined. 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 O. popup.nrat_date 2023-01-12 Close