Fuzzy Nilpotent Ideals in BCK-Algebras

One of the most critical concepts in the study of groups is the notion of nilpotency. Nilpotent groups arise in Galois theory, as well as in the classification of groups. In this paper, we apply the notion of nilpotency on BCK-algebras by using fuzzy ideals. First we define the concept of nilpotent fuzzy ideal in BCK-algebras and investigate their properties. Furthermore, we find some relation between fuzzy nilpotent ideals and quotient BCK-algebras. Specially, we construct a nilpotent BCK-algebra by using a fuzzy nilpotent ideal. Finally, we prove that any minimal ideals of a BCK-algebra X, is contained in the center of any fuzzy nilpotent ideals of X.