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The lattice of varieties of monoids

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Abstract

We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.

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Acknowledgements

The authors are indebted to the following colleagues: the anonymous reviewers for valuable suggestions, Marcel Jackson and Olga Sapir for very helpful discussions, and Mikhail Volkov for important information on pseudovarieties in Sub-sect. 1.2.

The first and third authors were supported by the Ministry of Science and Higher Education of the Russian Federation (project FEUZ-2020-0016).

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Authors and Affiliations

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

    Sergey V. Gusev & Boris M. Vernikov

  2. Department of Mathematics, Nova Southeastern University, Fort Lauderdale, Florida, 33314, USA

    Edmond W. H. Lee

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  1. Sergey V. Gusev
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  2. Edmond W. H. Lee
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  3. Boris M. Vernikov
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Communicated by: Toshiyuki Kobayashi

In memory of Professor Lev N. Shevrin (1935–2021)

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Gusev, S.V., Lee, E.W.H. & Vernikov, B.M. The lattice of varieties of monoids. Jpn. J. Math. 17, 117–183 (2022). https://doi.org/10.1007/s11537-022-2073-5

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