Characterization of Regularity of Posemigroups by High-Quasi-Ideals

A semigroup S is called a posemigroup if S is equipped with an ordering relation\ ≤ " such that a ≤ b in S implies xa ≤ xb and ax ≤ bx, for all x ۲ S. In what followswe study necessary and sufficient conditions that a posemigroup S to be regular, interms of certain conditions of Q∗ S, the semigroup of high-quasi-ideals of S. This studygives us a characterization method of the regular posemigroups.

Keywords:

Posemigroup , Regular , High-quasi-ideal , High-bi-ideal