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

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