Maximal residuated lattices with lifting Boolean center

TL;DR

This paper introduces a class of maximal residuated lattices with lifting Boolean center, inspired by ring theory, and proves they decompose into finite products of local residuated lattices.

Contribution

It defines the class of maximal residuated lattices with lifting Boolean center and establishes a structure theorem for their decomposition.

Findings

Maximal residuated lattices with lifting Boolean center are isomorphic to finite products of local residuated lattices.

The paper provides a structure theorem analogous to ring theory.

This advances understanding of the structure of residuated lattices.

Abstract

In this paper we define, inspired by ring theory, the class of maximal residuated lattices with lifting Boolean center and prove a structure theorem for them: any maximal residuated lattice with lifting Boolean center is isomorphic to a finite direct product of local residuated lattices.