On Coherent Filters of Pseudo-Complemented Almost Distributive Lattices

Abstract

In a pseudo-complemented Almost Distributive Lattice (pseudo-complemented ADL), the notions of coherent filters, strongly coherent filters, ♦-closed filters are introduced and their properties are studied. A set of equivalent conditions for any filter of a pseudo- complemented ADL to become a coherent filter is given. Also, the concept of median filters is introduced and a set of equivalent conditions for any maximal filter of a pseudo-complemented ADL to become a median filter is derived which leads to the characterization of a stone ADL.

Keywords: strongly coherent filter; median filter;minimal prime filter; maximal filter; stone ADL.

2010 Mathematics Subject Classification. 06D99; 06D15