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... more
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 T3 and 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.
