International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 6, Pages 387-389
doi:10.1155/S0161171201010997
Abstract
A groupoid G whose elements satisfy the left invertive law:
(ab)c=(cb)a is known as Abel-Grassman's groupoid (AG-groupoid).
It is a nonassociative algebraic structure midway between a
groupoid and a commutative semigroup. In this note, we show that
if G is a finite AG-groupoid with a left zero then, under
certain conditions, G without the left zero element is a commutative group.