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The connection of skew Boolean algebras and discriminator varieties to Church algebras

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Abstract

We establish a connection between skew Boolean algebras and Church algebras. We prove that the set of all semicentral elements in a right Church algebra forms a right-handed skew Boolean algebra for the properly defined operations. The main result of this paper states that the variety of all semicentral right Church algebras of type \({\tau}\) is term equivalent to the variety of right-handed skew Boolean algebras with additional regular operations. As a corollary to this result, we show that a pointed variety is a discriminator variety if and only if it is a 0-regular variety of right-handed skew Boolean algebras.

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Authors and Affiliations

  1. Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000, Ljubljana, Slovenia

    Karin Cvetko-Vah

  2. Department of Environmental Sciences, Informatics andStatistics, Università Ca’Foscari Venezia, Via Torino 155, 30172, Venezia, Italy

    Antonino Salibra

Authors
  1. Karin Cvetko-Vah
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  2. Antonino Salibra
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Correspondence to Antonino Salibra.

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Presented by J. Raftery.

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Cvetko-Vah, K., Salibra, A. The connection of skew Boolean algebras and discriminator varieties to Church algebras. Algebra Univers. 73, 369–390 (2015). https://doi.org/10.1007/s00012-015-0320-9

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  • DOI: https://doi.org/10.1007/s00012-015-0320-9

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