The Γ- permutation BCK-algebras with their Γ- permutation ideals

Abstract

In this work, we propose the notion of Γ- permutation BCK-algebras as an extension of BCK-algebras and investigate them. We also present Γ- permutation BCK-subalgebra, Γ- permutation BCK-ideal, Γ- permutation BCK-closed ideal, Γ- permutation normal BCK-subalgebra, Γ- permutation normal BCK-ideal, and quotient Γ- permutation BCK-algebra. We show that if h: X→Y is a normal homomorphism of Γ-permutation BCK-algebras X and Y, the quotient Γ-permutation BCK-algebra Y/V is isomorphic to Im(h), where V = ker(h).