Fuzzy Nilpotent Ideals in BCK-Algebras

Abstract

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 [Formula: see text]-algebras by using fuzzy ideals. First we define the concept of nilpotent fuzzy ideal in [Formula: see text]-algebras and investigate their properties. Furthermore, we find some relation between fuzzy nilpotent ideals and quotient [Formula: see text]-algebras. Specially, we construct a nilpotent [Formula: see text]-algebra by using a fuzzy nilpotent ideal. Finally, we prove that any minimal ideals of a [Formula: see text]-algebra [Formula: see text], is contained in the center of any fuzzy nilpotent ideals of [Formula: see text].