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Journals / Hacettepe Journal of Mathematics and Statistics / 2014 / Cilt: 43 - Sayı: 4

Fuzzy ?-ideals in ?-AG-groupoids

Tariq SHAH
Inayatur REHMAN
Asghar KHAN
Pages
625–634
Publication Date
2022-10-18
DOI
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⚡ TL;DR(Too Long; Didn't Read)

We also show that, if Sis a ?-AG-groupoid with left identity e, then every fuzzy ?-ideal of Sis prime if and only if every fuzzy ?-ideal of S is idempotent and theset of fuzzy ?-ideals of S is totally ordered by inclusion.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we study fuzzy ?-ideals and prime, semiprime fuzzy ?ideals of a ?-AG-groupoid S.
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Key Findings & Data:We prove that, if S is a ?-AG-groupoidwith left identity, then every fuzzy ?-ideal of S is idempotent if andonly if every fuzzy ?-ideal of S is semiprime.
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Conclusion & Impact:We also show that, if Sis a ?-AG-groupoid with left identity e, then every fuzzy ?-ideal of Sis prime if and only if every fuzzy ?-ideal of S is idempotent and theset of fuzzy ?-ideals of S is totally ordered by inclusion.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we study fuzzy ?-ideals and prime, semiprime fuzzy ?ideals of a ?-AG-groupoid S. We prove that, if S is a ?-AG-groupoidwith left identity, then every fuzzy ?-ideal of S is idempotent if andonly if every fuzzy ?-ideal of S is semiprime. We also show that, if Sis a ?-AG-groupoid with left identity e, then every fuzzy ?-ideal of Sis prime if and only if every fuzzy ?-ideal of S is idempotent and theset of fuzzy ?-ideals of S is totally ordered by inclusion.

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Cite This Article

SHAH, T., REHMAN, I., KHAN, A. (2022). Fuzzy ?-ideals in ?-AG-groupoids. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 4, 625–634. https://ajindex.com/articles/530380

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