Author(s):
1. M. Iqbal:
Department of Mathematics, University of Malakand,Chakdara, Dir(L),Pakistan
2. I. Ahmad:
Department of Mathematics, University of Malakand,Chakdara, Dir(L),Pakistan
Abstract:
An AG-groupoid that satisfies the identity a(bc) = c(ab) is called a CA-AG-groupoid [1]. In this article various properties of CA-AG-groupoids are explored and their relations with various other known subclasses of AG-groupoids and with some other algebraic structures are established. We proved that in CA-AG-groupoid left alternativity implies right alternativity and vice versa. We also proved that a CA-AG-groupoid having a right cancellative element is a T1, a T 3and an alternative AG-groupoid. We provided a partial solution to an open problem of right cancellative element of an AG-groupoid. Further, we proved that a CA-AG-groupoid having left identity is a commutative semigroup and investigated that the direct product of any two CA-AG-groupoids is again cyclic associative. Moreover, we investigated relation among CA, AG* and Stein AG-groupoids.
Page(s):
325-337
DOI:
DOI not available
Published:
Journal: Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, Volume: 53, Issue: 3, Year: 2016
Keywords:
Stein AGgroupoids
,
direct product
,
bicommutative
,
CAAGgroupoid
,
AGgroupoid
References:
[1] Iqbal M.,I. Ahmad M. .2016 .On Further Study of CA-AG-groupoids. Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 3 : 325-337.
Citations
Citations are not available for this document.