$γ$- BCK algebras - Arsham Borumand Saeid; M Murali Krishna Rao; R Kumar Kona (Journal of Mahani Mathematical Research)
We know that $Γ-$ring, $Γ-$incline, $Γ-$semiring, $Γ-$semigroup are generalizations ofring, incline, semiring and semigroup respectively. In this paper, we introduce the concept of $Γ-$BCK-algebras as a generalization of BCK-algebras and study $Γ-$BCK-algebras. We also introduce subalgebra, ideal, closed ideal, normal subalgebra, normal ideal and construct quotient of $Γ-$BCK-algebras. We prove that if $f: M→ L$ be a normal homomorphism of $Γ-$BCK-algebras $M$ and $N,$ then $Γ-$BCK-algebra $M/N$ is isomorphic to $Im (f)$ where $N =Ker (f).$