# MVW-rigs

## TL;DR

This paper introduces MVW-rigs, a novel algebraic structure combining MV-algebras with a product operation, exploring their properties, examples, and parallels to ring theory, including prime spectra and topological aspects.

## Contribution

It defines MVW-rigs with universal algebra axioms, provides natural examples, and establishes foundational results on ideals, quotients, homomorphisms, and prime spectra.

## Key findings

- Prime spectrum of MVW-rigs is compact with co-Zariski topology.
- Analogies between MVW-rigs and commutative rings are developed.
- Foundational algebraic properties of MVW-rigs are established.

## Abstract

In this paper, a new algebraic structure is defined, which is a new MV-algebra that has a product operation, we will call it MVW-rig (Multivalued-weak rig). This structure is defined with universal algebra axioms, it is presented with a good amount of natural examples in the MV-algebra environment and the first results having to do with ideal, quotients, homomorphisms and subdirect product are established. In particular, its prime spectrum is studied, that with the co-Zariski topology it is compact. Consequently, a good number of results that are analogous to the theory of commutative rings and rigs are presented with which this theory keeps a close relationship to.