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Information × Registration Number 0225U003662, (0122U000820) , R & D reports Title Free Lode structures and monoids of endomorphisms popup.stage_title Вільні структури Лоде та моноїди ендоморфізмів Head Zhuchok Anatolii V., д.ф.-м.н. Registration Date 28-07-2025 Organization State establishment "Luhansk Taras Shevchenko national University" popup.description1 Fundamental research on the most important problems of the theory of universal algebra, modern semigroup theory and graph theory - areas of mathematics, which are currently most actively developing. popup.description2 Report on research work (28 pages) STRICT N-FOLD SEMIGROUPS, DOPPELSEMIGROUPS, SEMIGROUPS, DIGROUPS, TRIODES, DIMONOIDS, SEMIGROUPS OF ENDOMORPHISMS, FREE ALGEBRA. Object of study: n-fold semigroups and related algebraic structures. Subject of study: the structure of these systems and their semigroups of endomorphisms. Purpose of study: fundamental study of the structural theory of universal algebras and semigroups, preparation of publications in professional Ukrainian and foreign journals. Research methods: general algebra, group theory, trioid theory, dopel semigroups, combinatorial analysis; decompositions, graph methods (Bottcher–Knaur), image theory, description of automorphisms (Plotkin's method). Novelty of results: for the first time, new constructive and factorization models have been constructed for free trioids, dimonoids, digroups, and n-fold semigroups. Congruences have been investigated and the corresponding endomorphisms have been described. The endotype method has been applied to classify equivalences. Degree of implementation: reports at conferences in Linz, Prague, Tartu, Bern, Ljubljana, Kyiv, Lviv, Potsdam, and other scientific forums. Interconnection with other works: “Structural properties of algebraic systems,” “Semigroups and dimonoids” (registration numbers 0109U001772, 0115U000199, and others). Recommendations for using the results of the work: the results are used in research on new types of algebras and graph structures; they are useful for mathematical centers, higher education institutions, students, and graduate students. Field of application: mathematics, educational process in higher education institutions.Economic efficiency: providing scientific and methodological support to teachers of mathematical disciplines. The significance of the work lies in the creation of new relatively free algebras and their application to the theories of 0-dialgebras, dialgebras, dopel algebras, and trialgebras. Product Description popup.authors Zhuchok Yuliia V. Zhuchok Yurii V. popup.nrat_date 2025-07-28 Close