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Information × Registration Number 0222U002356, 0119U100181 , R & D reports Title Free systems in the variety of n-tuple semigroups and endomorphism semigroups popup.stage_title Head Zhuchok Anatolii V., Доктор фізико-математичних наук Registration Date 11-02-2022 Organization State establishment "Luhansk Taras Shevchenko national University" popup.description2  Report on a research work: 21 p. N-TUPLE SEMIGROUP, DOPPELSEMIGROUP, SEMIGROUP, TRIOID, FREE ALGEBRA, SEMIGROUP OF ENDOMORPHISMS. The object of the research are n-tuple semigroups, doppelsemigroups, semigroups and trioids. The subject of the research are the structure of n-tuple semigroups, doppelsemigroups, semigroups and trioids and also semigroups of endomorphisms of the given algebras. The purpose of the research is to conduct the fundamental researches on the most important problems of the modern theory of universal algebras and semigroup theory which are the fields of mathematics currently developing most actively. Using the research results, prepare and publish the scientific articles in the specialized journals of Ukraine and foreign mathematical editions. Research methods: general algebraic methods with using the basic methods of the theory of semigroups, the theory of dimonoids, the theory of trioids, the combinatorial analysis, decomposition method, representation method, Bottcher-Knauer’s method of classification of undirected graphs by their endotype. The novelty of the results is that for the first time new relatively free algebras were substantiated and constructed in constructive and factorization ways, namely, some relatively free n-tuple semigroups, the free product of n-tuple semigroups and relatively free trioids were presented. Also congruences on these free algebras are investigated and semigroups of endomorphisms of some constructed free algebras are characterized. The structure and properties of the endotopism semigroups of the partial equivalence relation are described. The degree of an implementation is determined by the presentation of performers' results at foreign and domestic international conferences and scientific seminars: reports at the International Algebraic Conferences in Vienna (Austria), Siena (Italy), Krakow (Poland), Kiev (Ukraine), Vinnitsa (Ukraine) and other scientific events. Product Description popup.authors Zhuchok Anatoliy Volodymirovych Zhuchok Yuliia Volodymyrivna Zhuchok Yurii Volodymyrovych Kryklia Yana A Toichkina Olena O. popup.nrat_date 2022-03-09 Close