MORPHISMS AND PROPERTIES OF NON-ASSOCIATIVE ALGEBRAIC SYSTEMS WITH MOUFANG TYPE CONDITIONS

Abstract

The purpose and objectives of the thesis. The aim of the paper is to investigate the mor-phisms and properties of non-associative algebraic systems with Moufang-type identities. To achieve this goal, the following objectives have been defined: (1) research on the relations of 𝑊𝐴-, 𝐶𝐼-quasigroups, transitive on the left and Neumann with the quasigroups Moufang, Bol on the left, on the right, etc.; (2) research of quasigroups with any of the 60 classical Bol-Moufang identities listed in [12] at the existence of the unit; (3) research of morphisms, properties, relationships with other classes of quasigroups of newly defined quasigroups (i-quasigroups and 𝑂𝑊𝐼𝑃-quasigroups); (4) research on the G-properties of left transitive quasigroups and Neumann quasigroup.