Quasicomplemented residuated lattices

In this paper, the class of quasicomplemented residuated lattices is introduced and investigated, as a subclass of residuated lattices in which any prime filter not containing any dense element is a minimal prime filter. The notion of a disjunctive residuated lattice is introduced, and it is observed that a residuated lattice is Boolean if and only if it is disjunctive and quasicomplemented. Finally, some characterizations for quasicomplemented residuated lattices are given by means of the new notion of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-filters.