Semigroups under a sandwich operation

Abstract

For any element a of a semigroup (S,·), we may define a “sandwich” operation ∘ on the set S by x ∘ y = xay (x, y ∈ S). Under this operation the set S is again a semigroup; we denote this semigroup by (S, a) and call it a variant of S. Variants of semigroups of binary relations have been studied by Chase [6, 7]. In this paper we consider variants of arbitrary semigroups.