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

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2018

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Abstract (2. Language): 
ome well known results on ordered semigroups are examined in case of ordered hyper- semigroups. Following the paper in Semigroup Forum 44 (1992), 341{346, we prove the following: The ideals of an ordered hypergroupoid H are idempotent if and only if for any two ideals A and B of H, we have A \ B = (A  B]. 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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REFERENCES

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