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Complete Commutative Basic Algebras

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Abstract

By a basic algebra is meant an MV-like algebra (A, ⊕, ¬, 0) of type 〈2, 1, 0〉 derived in a natural way from bounded lattices having antitone involutions on their principal filters. In the previous paper (Botur and Halaš, Mult. Valued Log. Soft Comp., 2007) we have shown that finite basic algebras for which the operation ⊕ is commutative are MV-algebras. In this paper we generalize this result by considering commutative basic algebras for which the underlying lattice is complete.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00, Olomouc, Czech Republic

    Michal Botur & Radomír Halaš

Authors
  1. Michal Botur
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  2. Radomír Halaš
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Correspondence to Michal Botur.

Additional information

Research is supported by the Research and Development Council of Czech Government via project MSN 6198959214.

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Botur, M., Halaš, R. Complete Commutative Basic Algebras. Order 24, 89–105 (2007). https://doi.org/10.1007/s11083-007-9061-5

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  • DOI: https://doi.org/10.1007/s11083-007-9061-5

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