On methods of constructing AD-quasigroups

Abstract

We research T-quasigroups with AD identity and Schweitzer identity. The necessary and sufficient condition has been determined that in the T-quasigroup G of the form x • y=ϕ(x)+ψ(y), AD identity and the Schweitzer identity are true. We have used the concept of a special direct product of an topological Abelian group G and proved that a binary operation can be defined on the set G × G, such that the new algebraic structure is a non-associative topological quasigroups obeying medial, semimedial and AD laws.