Prime Filters In A Pseudocomplemented Semilattice

Abstract

In this paper, we study the prime filters of a bounded pseudocomplemented semilattice. We extend some of the results of $[3]$ to pseudocomplemented semilattices. It is observed that the set of all prime filters $\mathcal{P}$ of a pseudocomplemented semilattice $S$ is a topology, and it is $T_0$ and compact. We also obtain some necessary and sufficient conditions for the subspace of maximal filters to be normal.