Arsham Borumand Saeid - Department of pure Mathematics, Facultu of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
M Murali Krishna Rao - Department of Mathematics, Sankethika Institute of Tech. and Management, Visakhapatnam, ۵۳۰ ۰۴۱, India
R Kumar Kona - Department of Mathematics, GIS, GITAM (Deemed to be University), Visakhapatnam- ۵۳۰ ۰۴۵, A.P., India

We know that \Gamma-ring, \Gamma-incline, \Gamma-semiring, \Gamma-semigroup are generalizations ofring, incline, semiring and semigroup respectively. In this paper, we introduce the concept of \Gamma-BCK-algebras as a generalization of BCK-algebras and study \Gamma-BCK-algebras. We also introduce subalgebra, ideal, closed ideal, normal subalgebra, normal ideal and construct quotient of \Gamma-BCK-algebras. We prove that if f: M\to L be a normal homomorphism of \Gamma-BCK-algebras M and N, then \Gamma-BCK-algebra M/N is isomorphic to Im (f) where N =Ker (f).

(Gamma-)BCK-algebra, Quotient Gamma-BCK-algebra, Subalgebra, Ideal, (Closed, Normal) Ideal