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- Title
On le-semigroups.
- Authors
KEHAYOPULU, Niovi
- 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.
- Subjects
SEMIGROUPS (Algebra); GROUP theory; ABELIAN semigroups; SEMIGROUPS of operators; OPERATOR theory
- Publication
Turkish Journal of Mathematics, 2016, Vol 40, Issue 2, p310
- ISSN
1300-0098
- Publication type
Article
- DOI
10.3906/mat-1503-74