Abstract
In this paper we have discusses Γ-left, Γ-right, Γ-bi-, Γ-quasi-, Γ-interior and Γ-ideals in Γ-AG^{**}-groupoids and regular Γ-AG^{**}-groupoids. Moreover we have proved that the set of Γ-ideals in a regular Γ-AG^{**}-groupoid form a semilattice structure. Also we have characterized a regular Γ-AG^{**}-groupoid in terms of left ideals.
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