On Decompositions of Intra-Regular and Left Regular Ordered $\star$-Semigroups

Chong-Yih Wu

Abstract


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

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|ISSN 1686-0209|