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Information × Registration Number 0222U000610, 0122U000212 , R & D reports Title Researches of free trioids and endomorphism semigroups popup.stage_title Head Zhuchok Anatolii V., Доктор фізико-математичних наук Registration Date 14-01-2022 Organization State establishment "Luhansk Taras Shevchenko national University" popup.description2  FREE TRIOID, n-TRINILPOTENT TRIOID, n-TRINILPOTENT CONGRUENCE, ENDOMORPHISM SEMIGROUP. Objects of the research are n-trinilpotent trioids, free trioids, semigroups, binary relations. Subjects of the research are the structure of n-trinilpotent trioids, free trioids and endomorphism semigroups of these objects. The objective: conducting fundamental researches in such theories as the theory of dimonoids and trioids, the theory of dopelsemigroups and n-fold semigroups, the theory of semigroups, and a publication of results of these studies in professional scientific journals of Ukraine or international journals included in scientometric databases Scopus and/or Web of Science. Research results: cardinality of the free left (right) n-trinilpotent triods is calculated; idempotents of the free left (right) n-trinilpotent trioid are described; regular elements of the free left (right) n-trinilpotent trioid are described; the smallest left (right) n-trinilpotent congruence on the free trioid is characterized; the problem of attaching bar units to dimonoids of given classes is solved; the smallest dimonoid congruence and the smallest semigroup congruence on free (commutative, n-nilpotent) g-dimonoid are characterized; a free left (right) n-trinilpotent trioid is constructed; a free left (right) n-trinilpotent trioid is constructed; a free abelian trioid is constructed and the smallest abelian congruence on the free trioid is described; definability of partial equivalences by their endotopisms is studied; cardinalities of the endotopism semigroup, the strong endotopism monoid, and the autotopism group of a partial equivalence on a finite set are calculated; the classification of strict partial equivalences according to their endotype relative to endotopisms is obtained. 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 2022-03-09 Close