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Tolerances as images of congruences in varieties defined by linear identities

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Abstract

An identity s = t is linear if each variable occurs at most once in each of the terms s and t. Let T be a tolerance relation of an algebra \({\mathcal{A}}\) in a variety defined by a set of linear identities. We prove that there exist an algebra \({\mathcal{B}}\) in the same variety and a congruence θ of \({\mathcal{B}}\) such that a homomorphism from \({\mathcal{B}}\) onto \({\mathcal{A}}\) maps θ onto T.

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Authors and Affiliations

  1. Palacký University Olomouc, Department of Algebra and Geometry, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Ivan Chajda & Radomír Halaš

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

    Gábor Czédli

  3. Department of Mathematics, Tor Vergata University of Rome, I-00133, Rome, Italy

    Paolo Lipparini

Authors
  1. Ivan Chajda
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  2. Gábor Czédli
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  3. Radomír Halaš
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  4. Paolo Lipparini
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Corresponding author

Correspondence to Gábor Czédli.

Additional information

Presented by E. Kiss.

This research was supported the project Algebraic Methods in Quantum Logic, no. CZ.1.07/2.3.00/20.0051, and by the NFSR of Hungary (OTKA), grant numbers K77432 and K83219.

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Chajda, I., Czédli, G., Halaš, R. et al. Tolerances as images of congruences in varieties defined by linear identities. Algebra Univers. 69, 167–169 (2013). https://doi.org/10.1007/s00012-013-0219-2

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  • DOI: https://doi.org/10.1007/s00012-013-0219-2

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