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Information × Registration Number 0225U003092, (0122U001462) , R & D reports Title Algebraic systems, their derivative structures and the educational process in educational institutions popup.stage_title Алгебричні системи, їх похідні структури та освітній процес у закладах освіти Head Pypka Oleksandr O., Доктор фізико-математичних наук Registration Date 19-05-2025 Organization Oles Honchar Dnipro National University popup.description1 The aim of the work is to obtain a description of the structure and properties of some important algebraic systems (groups, algebras, etc.) with restrictions on their subsystems and their derivative structures (groups of automorphisms, algebras of differentiation, etc.); to form a system of teaching certain sections of school and higher mathematics. popup.description2 Report: 7 pages, 1 appendix. Keywords: LEIBNIZ ALGEBRA, BRACE, GROUP, MODULE, EDUCATION. The objects of the study are algebraic systems (algebras, groups, etc.) and the educational process. The subject of the study is the influence of natural subsystems on the structure of algebraic systems (groups, algebras, etc.); the impact of the properties of algebraic systems on the structure of their derivative structures; and the teaching of specific sections of school and higher mathematics in educational institutions. The aim of the study is to describe the structure and properties of certain important algebraic systems (groups, algebras, etc.) under given restrictions on their subsystems and derivative structures; and to develop a system for teaching selected topics in school and higher mathematics. Research methods - modern methods of algebra theory, group theory, module theory, brace theory, and contemporary approaches to studying educational issues in Ukraine. The conducted research resulted in a description of the structure and properties of certain important algebraic systems (groups, algebras, etc.) with specified restrictions on their subsystems and derivative structures; and the development of a system for teaching specific sections of school and higher mathematics. The obtained results have been implemented in the educational process. They serve as a significant supplement to relevant algebra courses and contribute to the advanced training of graduate students in the field of the research project. The results are directly related to research projects on Leibniz algebra theory, group theory, module theory, and brace theory conducted at universities in Ukraine, the USA, Italy, Spain, and other countries. The significance of the obtained results lies in their tangible advantages compared to those of researchers working within general algebra. The findings indicate promising directions for further research in group theory, algebra, module theory, and brace theory. Product Description popup.authors Halaiko Yuliia A. Kurdachenko Leonid A. Minaiev Pavlo Ye. Pypka Oleksandr O. Tushev Anatolii V. popup.nrat_date 2025-05-19 Close