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Completions of GBL-algebras: negative results

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Abstract.

We provide a simple sufficient criterion to show that a given variety of GBL-algebras does not admit (local) completions. As corollaries, we obtain that no variety of GBL-algebras containing Chang’s chain, no nontrivial variety of ℓ-groups, nor the variety of product algebras admit completions. The first result strengthens a result of Gehrke and Priestley.

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Authors and Affiliations

  1. College of Engineering and Computer Science, Australian National University, Canberra, 0200, ACT, Australia

    Tomasz Kowalski

  2. School of Computer Science and Information Systems, Birkbeck College, Malet Street, Bloomsbury, London, WC1E 7HX, UK

    Tadeusz Litak

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  1. Tomasz Kowalski
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  2. Tadeusz Litak
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Correspondence to Tomasz Kowalski.

Additional information

This paper is a belated gift to Professor Andrzej Wroński on his 65th birthday.

Received August 10, 2006; accepted in final form March 8, 2007.

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Kowalski, T., Litak, T. Completions of GBL-algebras: negative results. Algebra univers. 58, 373–384 (2008). https://doi.org/10.1007/s00012-008-2056-2

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  • DOI: https://doi.org/10.1007/s00012-008-2056-2

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