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Turkish Journal of Mathematics

Article Title

On $le$-semigroups

DOI

10.3906/mat-1503-74

Abstract

We characterize the idempotent ideal elements of the $le$-semigroups in terms of semisimple elements and we prove, among others, that the ideal elements of an $le$-semigroup $S$ are prime (resp. weakly prime) if and only if they form a chain and $S$ is intraregular (resp. semisimple). The corresponding results on semigroups (without order) can be also obtained as an application of the results of this paper. The study of $poe$-semigroups plays an essential role in the theory of fuzzy semigroups and the theory of hypersemigroups.

First Page

310

Last Page

316

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