On Fuzzy 2-absorbing Γ-ideals in Γ-rings

Abstract

The goal of this paper is to give a definition of a generalization of fuzzy prime $\Gamma $-ideals in $\Gamma $-rings by introducing fuzzy 2-absorbing $\Gamma $-ideals and fuzzy weakly completely 2-absorbing $\Gamma $-ideals of commutative $\Gamma $-rings and to give their properties. Furthermore, we give a diagram which transition between definitions of fuzzy 2-absorbing $\Gamma $-ideals of a $\Gamma $-ring. Finally, we introduce fuzzy quotient $\Gamma $-ring of $R$ induced by the fuzzy weakly completely 2-absorbing $\Gamma $-ideal is a $2$-absorbing $\Gamma $-ring.

Keywords

• 2-absorbing
• fuzzy 2-absorbing ideal
• fuzzy 2-absorbing Γ-ideal
• fuzzy weakly completely 2-absorbing Γ-ideal
• fuzzy K-2-absorbing Γ-ideal

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