Topological Properties of Prime Filters and Minimal Prime Filters on a Paradistributive Latticoid

Abstract

In this paper, we study the concepts of prime filters and minimal prime filters on a paradistributive latticoid (PDL) and discuss various results. In addition, we prove that the annihilator filter S• is equal to the intersection of all prime filters not containing S. Furthermore, we explore minimal prime filters and study certain results associated with them. We provide some equivalent conditions for a PDL to be relatively complemented. Additionally, we derive some topological properties of the space of prime filters and minimal prime filters.