Fuzzy Γ-ideals in Γ-AG-groupoids

Authors : Tariq SHAH, İnayatur REHMAN, Asghar KHAN

Pages : 625-634

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Publication Date : 2014-08-01

Article Type : Research Paper

Abstract :In this paper we study fuzzy Γ-ideals and prime, semiprime fuzzy Γideals of a Γ-AG-groupoid S. We prove that, if S is a Γ-AG-groupoid with left identity, then every fuzzy Γ-ideal of S is idempotent if and only if every fuzzy Γ-ideal of S is semiprime. We also show that, if S is a Γ-AG-groupoid with left identity e, then every fuzzy Γ-ideal of S is prime if and only if every fuzzy Γ-ideal of S is idempotent and the set of fuzzy Γ-ideals of S is totally ordered by inclusion. 
Keywords : Γ AG groupoids, Fuzzy sets, Fuzzy Γ ideals, Prime fuzzy Γ ideals, Band, Irreducible fuzzy Γ ideals