Co-Stone Residuated Lattices

Abstract

In this paper we present some applications of the reticulation of a residuated lattice, in the form of a transfer of properties between the category of bounded distributive lattices and that of residuated lattices through the reticulation functor. The results we are presenting are related to co-Stone algebras; among other applications, we transfer a known characterization of $m$-co-Stone bounded distributive lattices to residuated lattices and we prove that the reticulation functor for residuated lattices preserves a certain construction, that we conjecture to be the strongly co-Stone hull.