The variety of unary semigroups with associate inverse subsemigroup

Abstract

In [1] the authors introduced the notion of an associate inverse subsemigroup of a regular semigroup, extending the concept of an associate subgroup of a regular semigroup, first presented in [2]. The semigroups of these two classes admit axiomatic characterisations in terms of unary operations and can, therefore, be considered as unary semigroups. In this paper we introduce the notion of unary semigroup with associate inverse subsemigroup [with associate subgroup] and show that the classes of such unary semigroups form varieties.