Dense Elements and Classes of Residuated Lattices

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.

16 pages

Cited by in corpus (5)

• The Reticulation of a Universal Algebra
• Functorial Properties of the Reticulation of a Universal Algebra
• Congruence Boolean Lifting Property
• Boolean Lifting Property for Residuated Lattices
• Algebraic and Topological Results on Lifting Properties in Residuated Lattices