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Morfismele şi proprietăţile sistemelor algebrice neasociative cu condiţii de tip Moufang


Author: Diduric Natalia
Degree:doctor of physics and mathematics
Speciality: 01.01.06 - Mathematical logics, algebra and theory of numbers
Year:2000
Scientific adviser: Victor Şcerbacov
doctor habilitat, associate professor (docent), Institute of Mathematics and Computer Science
Institution: Institute of Mathematics and Computer Science

Status

The thesis was presented on the 0 --, 0000 at the meeting of the Scientific Council and now it is under consideration of the National Council.

Abstract

Adobe PDF document – 0.76 Mb / in romanian
Adobe PDF document – 0.74 Mb / in english

Thesis

CZU 512.548

Adobe PDF document 2.09 Mb / in romanian
97 pages

Summary

Morphisms and properties of non-associative algebraic systems with Moufang type conditions”, submitted by Diduric Natalia for obtaining the title of doctor in mathematical sciences in the specialty 111.03 - Mathematical Logic, Algebra and Number Theory. The thesis was developed at the State University of Moldova, Chisinau, 2021. Thesis structure: the thesis is written in Romanian and contains an introduction, four chapters, general conclusions and recommendations, 98 bibliographic titles, 95 pages (including 86 pages of basic text). The obtained results are published in 16 scientific papers. Keywords: quasigroup, loop, group, groupoid, isotope, automorphism, left unit, right unit, pseudo-automorphism, left Bol (right) quasigroup, Moufang quasigrup, -quasigroup, -quasigroup, -quasigroup, medial quasigroup, Neumann quasigroup, transitivity, -properties. Thesis field of study: algebra, in spesial, the theory of quasigroups with identities including Bol-Moufang-type identities, properties of non-associative algebraic systems. The purpose and objectives of the paper. The aim of the paper is to investigate the properties of non-associative algebraic systems with Bol-Moufang type identities. To achieve this goal, the following objectives have been defined: research on the relations of -, -quasigroups, transitive on the left and Neuman with the quasigroups Moufang, Bol on the left, on the right, etc .; research of quasigroups with any of the 60 classical Bol-Moufang identities listed in [1] at the existence of the unit; research of morphisms, properties, relationships with other classes of quasigroups of newly defined quasigroups (i-quasigroups and - generalized quasigroups); research on the -properties of left transitive quasigroups and Neumann. Scientific novelty and originality consist in obtaining new theoretical results. All the results presented in the thesis are new and original. Diverse classes of quasigroups known earlier (-,  -quasigroups, transitive left quasigroups, Neumann, etc.) were researched. Two new classes of quasigroups were introduced and researched (-quasigroups, -generalized quasigroups). Isotope group quasigroup classes were investigated. The properties of some classes of invertible quasigroups were described. Connections between the studied quasigroup classes and the classical quasigroups Moufang, Bol, etc. were investigated. The general forms of the automorphisms, pseudoautomorphisms and quasitomorphisms of these quasigroups were determined