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Multipotent GBL-algebras

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Abstract

We investigate GBL-algebras with the property that for every element a there is a positive integer n such that a n = a n+1. We show that varieties of GBL-algebras generated by such algebras are commutative. We also present examples showing that other conditions forcing commutativity will be hard to come by.

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Authors and Affiliations

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

    Anatolij Dvurečenskij

  2. Universitá degli Studi di Cagliari, Facolta delle Scienze Pedagogiche e Filosofiche, Via Is Mirrionis 1, I–09–123, Cagliari, Italy

    Tomasz Kowalski

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

Additional information

Presented by J. Raftery.

The first author acknowledges the University of Cagliari for the hospitality during his stay. The paper has been supported by the Center of Excellence SAS – Physics of Information – I/2/2005 and Quantum Technologies, the grant VEGA Nos. 2/6088/26 SAV and 2/0032/09, by ERDF OP R&D Project CE QUTE ITMS 262401022, by Science and Technology Assistance Agency under the contract No. APVV–0071–06, and by the Slovak–Italian Project 0016-08, Bratislava.

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Dvurečenskij, A., Kowalski, T. Multipotent GBL-algebras. Algebra Univers. 64, 25–38 (2010). https://doi.org/10.1007/s00012-010-0085-0

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  • DOI: https://doi.org/10.1007/s00012-010-0085-0

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