International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 6, Pages 387-389
doi:10.1155/S0161171201010997
Finite AG-groupoid with left identity and left zero
Qaiser Mushtaq
and M.S. Kamran
Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
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.