On the set of (b, c)-invertible elements

Abstract

Let b and c be two elements in a semigroup S. We first find some new equivalent conditions for a H-class to be a group and analyze its structure from the viewpoint of generalized inverses. Then a necessary and sufficient condition under which the set of (b, c)-invertible elements is a subsemigroup of S with the reverse order law holding for (b, c)-inverses is given. At last, we investigate the (b, c)-invertibility of a special triple product and provide a new criterion for the (b, c)-invertibility of an element.