Journal Name:
- European Journal of Pure and Applied Mathematics
Key Words:
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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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