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Equational theories as congruences of enriched monoids

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Abstract.

The problem of characterizing the lattices of equational theories is still unsolved. In this paper we describe a class \({\mathcal{K}}\) of monoids enriched by two unary operations and show that a lattice L is a lattice of equational theories if and only if L is isomorphic to a lattice of congruences of some enriched monoid belonging to \({\mathcal{K}}\).

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Science, Chui pr., 265a, Bishkek, 720071, Kyrghyz Republic

    A. M. Nurakunov

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  1. A. M. Nurakunov
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Correspondence to A. M. Nurakunov.

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To memory of Norbert Newrly

Received January 20, 2007; accepted in final form June 5, 2007.

The author was supported by INTAS grant 03-51-4110 and The Alexander von Humboldt Foundation.

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Nurakunov, A.M. Equational theories as congruences of enriched monoids. Algebra univers. 58, 357–372 (2008). https://doi.org/10.1007/s00012-008-2080-2

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  • DOI: https://doi.org/10.1007/s00012-008-2080-2

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