## Theory of Abel Grassmann's Groupoids

**Authors:** Madad Khan, Florentin Smarandache, Saima Anis

An AG-groupoid is an algebraic structure that lies in between a groupoid
and a commutative semigroup. It has many characteristics similar to that of a
commutative semigroup. If we consider x^2y^2= y^2x^2, which holds for all x, y in a
commutative semigroup, on the other hand one can easily see that it holds in an
AG-groupoid with left identity e and in AG**-groupoids. This simply gives that
how an AG-groupoid has closed connections with commutative algebras.
We extend now for the first time the AG-Groupoid to the Neutrosophic
AG-Groupoid. A neutrosophic AG-groupoid is a neutrosophic algebraic
structure that lies between a neutrosophic groupoid and a neutrosophic
commutative semigroup.

**Comments:** 208 Pages.

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### Submission history

[v1] 2015-07-16 09:28:54

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