The Chinese Remainder Theorem for strongly semisimple MV-algebras and lattice-groups

TL;DR

This paper extends the Chinese Remainder Theorem to strongly semisimple MV-algebras and lattice-groups, providing a significant strengthening of the classical result within these algebraic structures.

Contribution

It proves a strengthened version of the Chinese Remainder Theorem specifically for strongly semisimple MV-algebras and lattice-groups.

Findings

Chinese Remainder Theorem holds for all MV-algebras

Strengthened version applies to strongly semisimple structures

Enhances understanding of algebraic properties of MV-algebras

Abstract

An MV-algebra (equivalently, a lattice-ordered Abelian group with a distinguished order unit) is strongly semisimple if all of its quotients modulo finitely generated congruences are semisimple. All MV-algebras satisfy a Chinese Reminder Theorem, as was first shown by Keimel four decades ago in the context of lattice-groups. In this note we prove that the Chinese Remainder Theorem admits a considerable strengthening for strongly semisimple structures.