Notes on MV-modules over integral domains

TL;DR

This paper explores the structure of MV-modules over integral domains, establishing a connection with linear spaces and focusing on semisimple cases within ordered algebraic frameworks.

Contribution

It introduces a detailed study of MV-modules over semisimple, totally ordered integral domains and demonstrates an adjunction with a class of linear spaces, advancing the theoretical understanding.

Findings

Characterization of semisimple MV-modules over ordered integral domains

Establishment of an adjunction with linear spaces

Insights into the structure of MV-modules in ordered algebraic contexts

Abstract

An MV-module is an MV-algebra endowed with a scalar multiplication with scalars in a PMV-algebra (i.e. an MV-algebra endowed with a binary "ring-like" product). We investigate the class of semisimple MV-modules over a semisimple and totally ordered integral domain, and we prove an adjunction with a special class of linear spaces.