On some classes of noncommutative dimonoids

Abstract

The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative dimonoids, we construct a number of abelian, nonabelian, and rectangular dimonoids. The structure of these objects is analyzed, their automorphism groups and halos are computed.