Cancellative Elements in Finite AG-groupoids

Authors : Mehtab Khan, Amir Khan, Muhammad Uzair Khan

Pages : 53-56

View : 18 | Download : 10

Publication Date : 2020-03-26

Article Type : Research

Abstract :An Abel-Grassmann's groupoid (brie y AG-groupoid) is a groupoid S satisfying the left invertive law: (xy)z = (zy)x  for all x, y, z \in S. In the present paper, we discuss the left and right cancellative property of elements of the nite AG-groupoid S. For an AG-groupoid with left identity it is known that every left cancellative ele- ment is right cancellative. We prove a problem (for nite AG-groupoids) that every left cancellative element of an AG-groupoid (without left identity) is right cancella- tive. Moreover, we generalize various results of nite AG-groupoids by removing the condition of existence of left identity.
Keywords : AG-groupoid, AG-subgroupoid, Cancellative elements, non-cancellative elements