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Full dualisability is independent of the generating algebra

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Abstract

Given a full duality based on a finite algebra M, we show how to create a full duality based on any other finite algebra N for which \({\mathbb{ISP}({\bf M}) = \mathbb{ISP}({\bf N})}\). So the full dualisability of a quasivariety is independent of the algebra chosen as the generator. We obtain this result by proving the corresponding result for multisorted full dualities.

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Authors and Affiliations

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

    B. A. Davey & J. G. Pitkethly

  2. Faculty of Natural Sciences, M Bel University, Tajovského 40, 974 01, Banská Bystrica, Slovakia

    M. Haviar

Authors
  1. B. A. Davey
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  2. M. Haviar
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  3. J. G. Pitkethly
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Corresponding author

Correspondence to B. A. Davey.

Additional information

Presented by M. Ploscica.

The first and third authors thank the Research Institute of M. Bel University, Banská Bystrica, for its hospitality during the preparation of this paper. The second author acknowledges support from Slovak grant VEGA 1/0485/09. The third author acknowledges the support of a Charles La Trobe Postdoctoral Fellowship.

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Davey, B.A., Haviar, M. & Pitkethly, J.G. Full dualisability is independent of the generating algebra. Algebra Univers. 67, 257–272 (2012). https://doi.org/10.1007/s00012-012-0180-5

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  • DOI: https://doi.org/10.1007/s00012-012-0180-5

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