γ−bck-algebras

We know that γ−ring, γ−incline, γ−semiring, γ−semigroup are generalizations of ring, incline, semiring and semigroup respectively. in this paper, we introduce the concept of γ−bck-algebras as a general-ization of bck-algebras and study γ−bck-algebras. we also introduce subalgebra, ideal, closed ideal, normal subalgebra, normal ideal and con-struct 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).