Some Basic Properties of Γ-Abel-Grassmann's Groupoids
Keywords:
Γ-AG-groupoid, Γ-AG*-groupoid, Γ-AG**-groupoid, Γ-cancellative AG*-groupoid, Γ-Bol*-AG-groupoid.Abstract
In this article we investigate some basic properties of newly discovered classes of Γ-AG-groupoids. We consider three classes that include Γ-AG*-groupoids, -middle nuclear square AG-groupoids, Γ-right nuclear square AG-groupoids and Γ-Bol*-AG-groupoids. We start with the following theorem that gives a relation between Γ-AG*-groupoids, Γ-middle nuclear square and Γ- nuclear square. We investigate that every Γ-cancellative AG*-groupoid is Γ-transitively commutative AG-groupoid.
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