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Tolerances as images of congruences in varieties defined by linear identities |
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| Authors: | Ivan Chajda Gábor Czédli Radomír Halaš Paolo Lipparini |
| Affiliation: | 1. Palacky University Olomouc, Department of Algebra and Geometry, 17. listopadu 12, 771 46, Olomouc, Czech Republic 2. University of Szeged, Bolyai Institute, Aradi vértanúk tere 1, Szeged, 6720, Hungary 3. Department of Mathematics, Tor Vergata University of Rome, I-00133, Rome, Italy |
| 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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