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Information × Registration Number 0218U003316, 0115U000199 , R & D reports Title Semigroups and structural properties of dimonoids popup.stage_title Head Zhuchok Anatolii Volodymyrovych, Доктор фізико-математичних наук Registration Date 31-01-2018 Organization State Institution Luhansk Taras Shevchenko National University popup.description2 Report on a research work: 24 p. The object of the research are dimonoids, g-dimonoids and digroups, semigroups and doppelsemigroups, trioids. The subject of the research are the structure of dimonoids and digroups, semigroups and doppelsemigroups, g-dimonoids and trioids, the properties of semigroups of endomorphisms of free dimonoids, g-dimonoids and trioids. The purpose of the research is the fundamental researches on the most important problems of the modern theory of dimonoids, g-dimonoids, digroups, trioids and doppelsemigroups which is the field of mathematics, сonstruct a series of new relatively free algebras and investigate their properties. 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, L.M. Gluskin's method for obtaining the characteristics of semigroups of transformations, the method of G. Mashevitsky and B.M. Schein about the description of automorphisms of categories of free algebras. 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, congruences on these free algebras are investigated and semigroups of endomorphisms of some constructed free algebras are characterized. The degree of an implementation is determined by the presentation of performers' results at foreign and domestic international conferences and scientific seminars: Slovak Republic; Germany,Bulgaria; Belarus, Czech Republic etc.Interrelation with other works: "Application of algebraic-geometric methods in the theories of groups, semigroups, rings, representations to problems of applied algebra and information protection" (state registration number 0111U005264) which was carried out at Taras Shevchenko National University of Kyiv. Recommendations on using the results of the work: the obtained results can be used in studies of doppelalgebras, dialgebras, 0-dialgebras, trialgebras, dimonoids, trioids and semigroups. Application area: mathematics; the educational process of universities which train mathematicians, master's degree students and PhD students.Economic efficiency: the results of the work are of theoretical importance, they provide the scientific and methodological products on this subject for the university teachers.The significance of the work is to achieve the goal of the research in the construction of new relatively free algebras and their application to the theory of doppelalgebras, the theory of dialgebras and 0-dialgebras, the theory of trialgebras.Project assumptions about the development of the research object: the results of the research extend and supplement the structural theory of semigroups, and can be used in further studies to form the general theory of doppelsemigroups, to develop the theory of dialgebras and dimonoids, universal algebra, and to develop the theory of trioids. Keywords: dimonoid, g-dimonoid, digroup, semigroup, doppelsemigroup, trioid, free algebra, semigroup of endomorphisms. Product Description popup.authors Бондар Е. О. Горбатков О. Б. Жучок Ю. В. Жучок Юл. В. Мазяєва О. С. Тоічкіна О. О. popup.nrat_date 2020-04-02 Close