On fuzzy-Γ-ideals of Γ-Abel-Grassmann's groupoids

Details On fuzzy-Γ-ideals of Γ-Abel-Grassmann's groupoids On fuzzy-Γ-ideals of Γ-Abel-Grassmann's groupoids

2010-11-05

arxiv.org/abs/1011.1367v1

Mathematics

Group Theory

Scientific paper

In this paper, we have introduced the notion of {\Gamma}-fuzzification in {\Gamma}-AG-groupoids which is in fact the generalization of fuzzy AG-groupoids. We have studied several properties of an intra-regular {\Gamma}-AG^{**}-groupoids in terms of fuzzy {\Gamma}-left (right, two-sided, quasi, interior, generalized bi-, bi-) ideals. We have proved that all fuzzy {\Gamma}-ideals coincide in intra-regular {\Gamma}-AG^{**}-groupoids. We have also shown that the set of fuzzy {\Gamma}-two-sided ideals of an intra-regular {\Gamma}-AG^{**}-groupoid forms a semilattice structure.

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