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.
Primary Language | English |
---|---|
Subjects | Mathematical Sciences |
Journal Section | Research Article |
Authors | |
Publication Date | March 26, 2020 |
Submission Date | February 21, 2019 |
Published in Issue | Year 2020 Issue: 30 |
|