A Localization in MV-algebras

TL;DR

This paper explores a method for localizing MV-algebras by constructing local variants that preserve the structure of prime filters comparable to a given prime filter.

Contribution

It introduces a novel approach to localizing MV-algebras based on prime filters, expanding the understanding of their structural properties.

Findings

Established a construction for local MV-algebras from prime filters.

Showed the local MV-algebra shares the same prime filter poset as the original.

Provided insights into the structural relationships within MV-algebras.

Abstract

In this document we consider a way of localizing an MV-algebra. Given any prime filter $F$ we find a local MV-algebra which has the same poset of prime filters as the poset of prime filters comparable to $F$.