The product of quasi-ideal adequate transversals of an abundant semigroup

Abstract

An inverse transversal of a regular semigroup S is an inverse subsemigroup that contains precisely one inverse of each element of S. This concept was first introduced by Blyth and McFadden and generalized to an adequate transversal in the abundant case by El-Qallali. In this paper we show that the product of any two quasi-ideal adequate transversals of an abundant semigroup S which satisfy the regularity condition is a quasi-ideal adequate transversal of S. Furthermore, all adequate transversals of S form a rectangular band.