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The Chinese Remainder Theorem for Strongly Semisimple MV-Algebras and Lattice-Groups

Authors
  • Marra, Vincenzo
Type
Published Article
Journal
Mathematica Slovaca
Publisher
De Gruyter Open
Publication Date
Aug 01, 2015
Volume
65
Issue
4
Pages
829–840
Identifiers
DOI: 10.1515/ms-2015-0058
Source
De Gruyter
Keywords
License
Yellow

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 Remainder 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.

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