γ -fuzzy filters and space of γ -- fuzzy filters in P-algebra

Abstract

In this paper, we introduce the concept of γ−fuzzy filters in a pseudo-complemented distributive lattices. We study the special class of fuzzy filters called γ−fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of boosters. We observe that every γ−fuzzy filters is the intersection of all prime γ−fuzzy filters containing it. We also topologize the set of all prime γ−fuzzy filters of a pseudo-completed distributive lattice. Properties of the space also studied. We show that there is a one to one correspondence between the class of γ−fuzzy filters and the lattice of all open sets in Pγ. It is proved that the space Pγ is a T0 space.