On ordered hypersemigroups with idempotent ideals, prime and weakly prime ideals

Authors

  • Niovi Kehayopulu Professor Docent Dr. University of Athens

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i1.3085

Keywords:

ordered hypersemigroup, ideal, weakly prime, prime, idempotent, semisimple, left regular, intra-regular

Abstract

Some well known results on ordered semigroups are examined in case of ordered hypersemigroups. Following the paper in Semigroup Forum 44 (1992), 341--346, we prove the following: The ideals of an ordered hypergroupoidH are idempotent if and only if for any two ideals A and B of H, we have AB=(AB]. Let now H be an ordered hypersemigroup. Then, the ideals of H are idempotent if and only if H is semisimple. The ideals of H are weakly prime if and only if they are idempotent and they form a chain. The ideals of H are prime if and only if they form a chain and H is intra-regular. The paper serves as an example to show how we pass from ordered semigroups to ordered hypersemigroups.

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Published

2018-01-30

Issue

Section

Algebraic Geometry

How to Cite

On ordered hypersemigroups with idempotent ideals, prime and weakly prime ideals. (2018). European Journal of Pure and Applied Mathematics, 11(1), 10-22. https://doi.org/10.29020/nybg.ejpam.v11i1.3085