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Kites and pseudo BL-algebras

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Abstract

We investigate a construction of a pseudo BL-algebra out of an ℓ-group called a kite. We show that many well-known examples of algebras related to fuzzy logics can be obtained in that way. We describe subdirectly irreducible kites. As another application, we exhibit a new countably infinite family of varieties of pseudo BL-algebras covering the variety of Boolean algebras.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK–814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

  2. Department of Algebra and Geometry, Faculty of Sciences, Palacký University, tř. 17. listopadu 12, CZ-771 46, Olomouc, Czech Republic

    Anatolij Dvurečenskij

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

    Tomasz Kowalski

Authors
  1. Anatolij Dvurečenskij
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  2. Tomasz Kowalski
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Correspondence to Anatolij Dvurečenskij.

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Presented by J. Raftery.

The paper has been supported by the Center of Excellence SAS - Quantum Technologies, meta-QUTE ITMS 26240120022, Slovak Research and Development Agency under the contract APVV-0178-11, the grant VEGA No. 2/0059/12 SAV, and by CZ.1.07/2.3.00/20.0051.

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Dvurečenskij, A., Kowalski, T. Kites and pseudo BL-algebras. Algebra Univers. 71, 235–260 (2014). https://doi.org/10.1007/s00012-014-0276-1

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  • DOI: https://doi.org/10.1007/s00012-014-0276-1

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