Principally ordered regular semigroups
T. S. Blyth, Gama Pinto · Glasgow Mathematical Journal · 1990
An ordered semigroup S will be called principally ordered if, for every x ɛ S, there exists x* = max {y ɛ S; xyx ≤ x}. Here we shall be concerned with the case where S is regular. We begin by listing some basic properties that arise from the above definition. As usual, we shall denote by V(x) the set of inverses of x ɛ S.