Sandwich semigroups and Brandt semigroups

Abstract

In this paper we study a connection between variants of semigroups and Brandt semigroups. We find necessary conditions under which a variant of a semigroup is a Brandt semigroup. For variants of Rees matrix semigroups we studied a structure of a sandwich matrix. We proved that if semigroup does not contain a bicyclic subsemigroup, then any variant of this semigroup is not a Brandt semigroup. Thus a variant of a finite semigroup is not a Brandt semigroup.