Naturally ordered regular semigroups with maximum inverses

Abstract

Let S be a regular semigroup. An inverse subsemigroup S ° of S is called an inverse transversal if S ° contains a unique inverse of each element of S . An inverse transversal S ° of S is called multiplicative if x°xyy° is an idempotent of S ° for every x, y ∈ S , where x ° denotes the unique inverse of x ∈ S in S °. In Section 1, we obtain a necessary and sufficient condition in order for inverse transversals to be multiplicative.