n-fold 2-nilpotent(solvable) ideal of a BCK-algebra

In this paper, first we introduce the notions of k-nilpotent (solvable) ideals and BCK-algebras. Specially, show that every commutative ideal is 1-nilpotent (solvable). Second, state an equivalent condition to k-nilpotency (solvablity) BCK-algebra. Finally, study n-fold 2-nilpotent BCK-algebras as a generalization BCK-algebras, relation between these two concepts. Basically, compare solvable (BCK-algebras).