A, [cross product]) is a commutative semigroup
with ([for all] x [member of] A) (x [cross product] x = x), where the semigroup operation is strongly extensional:
An Abel- Grassmann's groupoid, abbreviated as an AG-groupoid (or in some papers left almost semigroup), is a non-associative algebraic structure mid way between a groupoid and a commutative semigroup
Let G be a Smarandache Groupoid, G is said to be a Smarandache commutative groupoid if there is a proper subset, which is a semigroup, is a commutative semigroup
3) For all e [member of] E(S),eSe is a commutative semigroup
In commutative semigroup
the prime and weakly Prime ideals coincide.