Notes on regular filters in residuated lattices

Abstract

In the mathematical literature, many types of filters in residuated lattices
have been studied. In [2] we proposed a new approach for the study of these filters. In this paper, in the spirit of [3], we establish some connections between regular filters and other types of filters in residuated lattices. Also, we prove that a residuated lattice is a Stonean residuated lattice if and only if every filter is a Stonean filter and we show that a residuated lattice has the Double Negation Condition if and only if every filter is a regular filter.