Scalar extensions for algebraic structures of Lukasiewicz logic

TL;DR

This paper investigates tensor products in MV-algebras, establishing their preservation under categorical equivalence and proving scalar extension properties, with implications for algebraic structures in Lukasiewicz logic.

Contribution

It proves tensor product preservation under categorical equivalence and establishes scalar extension properties for semisimple MV-algebras, advancing the algebraic understanding of Lukasiewicz logic.

Findings

Tensor product preserved by categorical equivalence

Scalar extension property for semisimple MV-algebras

Implications for classes of MV-algebras and lattice-ordered groups

Abstract

In this paper we study the tensor product for MV-algebras, the algebraic structures of \L ukasiewicz $\infty$-valued logic. Our main results are: the proof that the tensor product is preserved by the categorical equivalence between the MV-algebras and abelian lattice-order groups with strong unit and the proof of the scalar extension property for semisimple MV-algebras. We explore consequences of this results for various classes of MV-algebras and lattice-ordered groups enriched with a product operation.