Mighty filters in BE-algebras

Abstract

The notion of a mighty (vague) filter in a $BE$-algebra is introduced, and the relation between a (vague) filter and a mighty (vague) filter are given. We investigate an equivalent condition for a (vague) filter to be mighty, and state an extension property for mighty filter. Also we define the notion of an $n$-fold mighty filter which is an extended notion of a mighty filter in a $BE$-algebra. Characterizations of an $n$-fold mighty filter are given. Extension property for an $n$-fold mighty filter are provided.