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Studia Logica

, Volume 107, Issue 6, pp 1135–1158 | Cite as

Categorical Equivalence Between \(\varvec{PMV}_{\varvec{f}}\)-Product Algebras and Semi-Low \(\varvec{f}_{\varvec{u}}\)-Rings

  • Lilian J. CruzEmail author
  • Yuri A. Poveda
Article

Abstract

An explicit categorical equivalence is defined between a proper subvariety of the class of \({ PMV}\)-algebras, as defined by Di Nola and Dvurečenskij, to be called \({ PMV}_{f}\)-algebras, and the category of semi-low \(f_u\)-rings. This categorical representation is done using the prime spectrum of the \({ MV}\)-algebras, through the equivalence between \({ MV}\)-algebras and \(l_u\)-groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low \(f_u\)-rings associated to Boolean algebras are characterized.

Keywords

\({ PMV}\)-algebra \({ PMV}_{f}\)-algebra \(l_u\)-ring Prime ideal Spectrum 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Universidad del ValleCaliColombia
  2. 2.Universidad Tecnológica de PereiraPereiraColombia

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