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On prime, weakly prime ideals in po-Γ-semigroups

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Abstract

It is well known that the ideals of an ordered semigroup S are weakly prime if and only if they are idempotent, equivalently, if A ∩ B = (AB] for all ideals A,B of S. The ideals of an ordered semigroup S are prime if and only if they form a chain and S is intra-regular. These results have been examined already in case of both sided ordered Γ-semigroups considering the first definition of a Γ-semigroup introduced by Sen in 1981. In the present paper we keep the second definition of a Γ-semigroup introduced by Sen and Saha in 1986 (which is more general than the first one) and show that the results on ordered semigroups mentioned above can be extended to ordered Γ-semigroups without any additional conditions.

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Authors and Affiliations

  1. Department of Mathematics, University of Athens, 15784, Panepistimiopolis, Athens, Greece

    Niovi Kehayopulu

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  1. Niovi Kehayopulu
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Correspondence to Niovi Kehayopulu.

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Submitted by M.M.Arslanov

This work has been supported by the Special Research Account of the University of Athens (Grant No. 70/4/5630).

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Kehayopulu, N. On prime, weakly prime ideals in po-Γ-semigroups. Lobachevskii J Math 30, 257–262 (2009). https://doi.org/10.1134/S1995080209040027

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  • DOI: https://doi.org/10.1134/S1995080209040027

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