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

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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.

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Authors and Affiliations

  1. Universidad del Valle, Cali, Colombia

    Lilian J. Cruz

  2. Universidad Tecnológica de Pereira, Pereira, Colombia

    Yuri A. Poveda

Authors
  1. Lilian J. Cruz
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  2. Yuri A. Poveda
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Correspondence to Lilian J. Cruz.

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Presented by Daniele Mundici

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Cruz, L.J., Poveda, Y.A. Categorical Equivalence Between \(\varvec{PMV}_{\varvec{f}}\)-Product Algebras and Semi-Low \(\varvec{f}_{\varvec{u}}\)-Rings. Stud Logica 107, 1135–1158 (2019). https://doi.org/10.1007/s11225-018-9832-6

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  • DOI: https://doi.org/10.1007/s11225-018-9832-6

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