Ordered semigroups having the P-property
Niovi Kehayopulu, Michael Tsingelis · Russian Mathematics · 2008
In this paper we obtain the following main results. The ordered semigroups which have the P-property are decomposable into archimedean semigroups. Moreover, they are decomposable into semigroupswith the P-property. Conversely, if an ordered semigroup S is a complete semilattice of semigroups which have the P-property, then S itself also has the P-property. An ordered semigroup is CS-indecomposable and has the P-property if and only if it is archimedean. If S is an ordered semigroup, then the relation N:= {(a, b) | N(a) = N(b)} (here N(a) is a filter of S generated by a (a ∈ S)) is the least complete semilattice congruence on S and the class (a) N is a CS-indecomposable subsemigroup of S for each a ∈ S. We introduce the notion of the P m -property and describe it in terms of the P-property. Our approach simplifies the proofs of the corresponding results about unordered semigroups.