On Decompositions of Intra-Regular and Left Regular Ordered ?-Semigroups

Chong-Yih Wu

Abstract

Let S be an intra-regular or left (resp. right) regular ordered ?-
semigroup with order preserving involution ?. Structure theorems referring to the
decompositions of such semigroups into their simples subsemigroups are developed.
Also in view of semilattice congruences we characterize intra-regular ordered ?-
semigroups in which any two ideals are comparable under inclusion relation ⊆.