General coupled semirings of residuated lattices

TL;DR

This paper extends the known correspondence between MV-algebras and coupled semirings to a broader class of residuated lattices that satisfy the double negation law, enriching the algebraic framework.

Contribution

It generalizes the one-to-one correspondence from MV-algebras to residuated lattices with the double negation law, broadening the algebraic connections.

Findings

Established a correspondence between residuated lattices and coupled semirings.

Extended the algebraic framework beyond MV-algebras.

Provided theoretical foundations for further algebraic studies.

Abstract

Di Nola and Gerla showed that MV-algebras and coupled semirings are in a natural one-to-one correspondence. We generalize this correspondence to residuated lattices satisfying the double negation law.