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