Abstract
In the lattice of semigroup varieties, the set of all neutral elements is finite, the set of all distributive elements is countably infinite, and the set of all lower-modular elements is uncountably infinite. It was established in 2018 that the lattice of monoid varieties contains exactly three neutral elements. This article shows that neutrality, distributivity, and lower-modularity coincide in the lattice of monoid varieties. Thus, there exists only three varieties that are distributive and lower-modular elements of this lattice.
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Acknowledgment
The author is grateful to the referee for a series of useful remarks.
Funding
The author was supported by the Ministry of Science and Higher Education of the Russian Federation (Project FEUZ–2020–0016).
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 6, pp. 1248–1255. https://doi.org/10.33048/smzh.2022.63.606
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Gusev, S.V. Distributive and Lower-Modular Elements of the Lattice of Monoid Varieties. Sib Math J 63, 1069–1074 (2022). https://doi.org/10.1134/S0037446622060064
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DOI: https://doi.org/10.1134/S0037446622060064