Dense Elements and Classes of Residuated Lattices

TL;DR

This paper investigates the structure of dense elements, radicals, and various classes of residuated lattices, including BL-algebras and Glivenko residuated lattices, focusing on their lifting Boolean centers and related properties.

Contribution

It characterizes the dense elements, radicals, and Boolean center properties of residuated lattices, especially BL-algebras and Glivenko residuated lattices, expanding understanding of their algebraic structure.

Findings

BL-algebras have lifting Boolean center

Glivenko residuated lattices satisfying a specific equation also have lifting Boolean center

The paper classifies residuated lattices into simple, local, semilocal, and quasi-local types

Abstract

In this paper we study the dense elements and the radical of a residuated lattice, residuated lattices with lifting Boolean center, simple, local, semilocal and quasi-local residuated lattices. BL-algebras have lifting Boolean center; moreover, Glivenko residuated lattices which fulfill a certain equation (that is satisfied by BL-algebras) have lifting Boolean center.