Prime Filters In A Pseudocomplemented Semilattice

P. Balasubramanie1, R. Viswanathan2
1Department of Computer Science & Engineering-PG
2Department of Mathematics Kongu Engineering College, Perundurai, Erode – 638 052.

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.

Keywords: Prime filters, maximal filters, stone topology, compact space, normal space.