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Maximal Subalgebras of MVn-algebras. A Proof of a Conjecture of A. Monteiro

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Abstract

For each integer n ≥ 2, MVn denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MVn are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in MVn are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A ∈ MV3, the mentioned characterization of maximal subalgebras of A can be given in terms of prime filters of the underlying lattice of A, in the form that was conjectured by A. Monteiro.

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Authors and Affiliations

  1. Instituto Argentino de Matemática, CONICET, Saavedra 15, Piso 3, 1083, Buenos Aires, Argentina

    Roberto Cignoli

  2. INMABB-CONICET, Universidad Nacional del Sur, Avda. Alem 1253, 8000, Bahía Blanca, Argentina

    Luiz Monteiro

Authors
  1. Roberto Cignoli
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  2. Luiz Monteiro
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Correspondence to Roberto Cignoli.

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Mathematics Subject Classification (2000): 06D30, 06D35, 03G20, 03B50, 08A30.

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Cignoli, R., Monteiro, L. Maximal Subalgebras of MVn-algebras. A Proof of a Conjecture of A. Monteiro. Stud Logica 84, 393–405 (2006). https://doi.org/10.1007/s11225-006-9020-y

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  • DOI: https://doi.org/10.1007/s11225-006-9020-y

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