Ordered semigroups having the <Emphasis Type="Italic">P</Emphasis>-property |
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Authors: | N Kehayopulu M Tsingelis |
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Institution: | (1) Panepistimiopolis, University of Athens, GR-157 84 Athens, Greece |
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Abstract: | 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.
The text was submitted by the authors in English. |
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Keywords: | archimedean ordered semigroup P-property complete semilattice of a semigroup of the type T ideal filter CS-indecomposable ordered semigroup Pm-property |
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