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Two weaker variants of congruence permutability for monoid varieties

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Abstract

We completely determine all varieties of monoids on whose free objects all fully invariant congruences or all fully invariant congruences contained in the least semilattice congruence permute. Along the way, we find several new monoid varieties with the distributive subvariety lattice (only a few examples of varieties with such a property are known so far).

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  • 07 June 2021

    The original article has been updated to correct Reference 8.

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Authors and Affiliations

  1. Institute of Natural Sciences and Mathematics, Ural Federal University Lenina 51, Ekaterinburg, Russia, 620000

    Sergey V. Gusev & Boris M. Vernikov

Authors
  1. Sergey V. Gusev
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  2. Boris M. Vernikov
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Correspondence to Sergey V. Gusev.

Additional information

Communicated by Edmond W. H. Lee.

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The work was supported by the Ministry of Science and Higher Education of the Russian Federation (Project FEUZ-2020-0016).

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Gusev, S.V., Vernikov, B.M. Two weaker variants of congruence permutability for monoid varieties. Semigroup Forum 103, 106–152 (2021). https://doi.org/10.1007/s00233-021-10196-9

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  • DOI: https://doi.org/10.1007/s00233-021-10196-9

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