On CM-groupoids with multiple identities and medial topological left loops

Abstract

This paper studies some properties of CM-groupoids with multiple identities and medial topological left loops. The conditions for a CM-groupoid to become a CM-quasigroup were found. A new method of constructing non-associative medial topological quasigroups with left identity is given. Various examples of quasigroups with multiple identities have been constructed