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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
It is proved that a po-Γsemigroup S with a zero 0 is 0-(0, 2)-bisimple if and only if it is left 0-simple.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups.
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Key Findings & Data:Then we characterize the po-Γ-semigroup through ordered (generalized) (0, 2)-Γ-ideals, ordered (generalized) (1, 2)-Γ-ideals and ordered (generalized) 0-minimal (0, 2)-Γ-ideals.
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Conclusion & Impact:It is proved that a po-Γsemigroup S with a zero 0 is 0-(0, 2)-bisimple if and only if it is left 0-simple.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:po-Γ-semigroup · ordered bi-Γ-ideal · ordered(m
Abstract
In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups. Then we characterize the po-Γ-semigroup through ordered (generalized) (0, 2)-Γ-ideals, ordered (generalized) (1, 2)-Γ-ideals and ordered (generalized) 0-minimal (0, 2)-Γ-ideals. Also, we investigate the notion of ordered (generalized) (0, 2)-bi-Γ-ideals, ordered 0-(0, 2) bisimple po-Γ-semigroups and ordered 0-minimal (generalized) (0, 2)-bi-Γ-ideals in po-Γ-semigroups. It is proved that a po-Γsemigroup S with a zero 0 is 0-(0, 2)-bisimple if and only if it is left 0-simple.
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Cite This Article
Abbasi, M. Y., Basar, A. (2015). Some properties of ordered 0-minimal (0, 2)-bi-Γ-ideals in po-Γ-semigroups. Hacettepe Journal of Mathematics and Statistics, Volume: 44 Issue: 2. https://ajindex.com/articles/1403298