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Boolean-like algebras

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Abstract

Using Vaggione’s concept of central element in a double-pointed algebra, we introduce the notion of Boolean-like variety as a generalisation of Boolean algebras to an arbitrary similarity type. Appropriately relaxing the requirement that every element be central in any member of the variety, we obtain the more general class of semi-Boolean-like varieties, which still retain many of the pleasing properties of Boolean algebras. We prove that a double-pointed variety is discriminator if and only if it is semi-Boolean-like, idempotent, and 0-regular. This theorem yields a new Maltsev-style characterisation of double-pointed discriminator varieties.

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Authors and Affiliations

  1. Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’Foscari Venezia, Via Torino 155, 30172, Venezia Mestre, Italy

    Antonino Salibra

  2. Dipartimento di Pedagogia, Psicologia, Filosofia, Università di Cagliari, Via Is Mirrionis 1, 09123, Cagliari, Italy

    Antonio Ledda

  3. Dipartimento di Pedagogia, Psicologia, Filosofia, Università di Cagliari, Via Is Mirrionis 1, 09123, Cagliari, Italy

    Francesco Paoli

  4. Department of Mathematics and Statistics, La Trobe University, Victoria, 3086, Australia

    Tomasz Kowalski

Authors
  1. Antonino Salibra
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  2. Antonio Ledda
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  3. Francesco Paoli
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  4. Tomasz Kowalski
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Correspondence to Francesco Paoli.

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Presented by J. Berman.

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Salibra, A., Ledda, A., Paoli, F. et al. Boolean-like algebras. Algebra Univers. 69, 113–138 (2013). https://doi.org/10.1007/s00012-013-0223-6

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  • DOI: https://doi.org/10.1007/s00012-013-0223-6

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