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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
The study of $poe$-semigroups plays an essential role in the theory of fuzzy semigroups and the theory of hypersemigroups.
📌 3 Key Takeaways
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Objective & Hypothesis: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).
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Key Findings & Data:The corresponding results on semigroups (without order) can be also obtained as an application of the results of this paper.
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Conclusion & Impact:The study of $poe$-semigroups plays an essential role in the theory of fuzzy semigroups and the theory of hypersemigroups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$le$-semigroup · left (right) ideal element · ideal element
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.
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Cite This Article
KEHAYOPULU, N. (2016). On $le$-semigroups. Turkish Journal of Mathematics, Cilt: 40 - Sayı: 2, 310–316. https://ajindex.com/articles/723276