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Reflection-closed varieties of multisorted algebras and minor identities

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Abstract

The notion of reflection is considered in the setting of multisorted algebras. The Galois connection induced by the satisfaction relation between multisorted algebras and minor identities provides a characterization of reflection-closed varieties: a variety of multisorted algebras is reflection-closed if and only if it is definable by minor identities. Minor-equational theories of multisorted algebras are described by explicit closure conditions. It is also observed that nontrivial varieties of multisorted algebras of a non-composable type are reflection-closed.

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Authors and Affiliations

  1. Institut für Algebra, Technische Universität Dresden, 01062, Dresden, Germany

    Erkko Lehtonen & Reinhard Pöschel

  2. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720, Szeged, Hungary

    Tamás Waldhauser

Authors
  1. Erkko Lehtonen
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  2. Reinhard Pöschel
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  3. Tamás Waldhauser
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Corresponding author

Correspondence to Erkko Lehtonen.

Additional information

This article is part of the topical collection “The 5th Novi Sad Algebraic Conference (NSAC 2017)” edited by P. Marković, M. Maróti and A. Tepavčević.

Research supported by the Hungarian National Research, Development and Innovation Office (NKFIH Grant No. K115518).

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Lehtonen, E., Pöschel, R. & Waldhauser, T. Reflection-closed varieties of multisorted algebras and minor identities. Algebra Univers. 79, 70 (2018). https://doi.org/10.1007/s00012-018-0547-3

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  • DOI: https://doi.org/10.1007/s00012-018-0547-3

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