Geodesic
\large Equationally Noetherian varieties of semigroups and B.~Plotkin's problem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 724-734

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We consider systems of semigroup equations with constants. A semigroup $S$ is called equationally Noetherian if any system of equations is equivalent over $S$ to a finite subsystem. In the current paper we describe all semigroup varieties that consist of equationally Noetherian semigroups. Our result solves the problem of B.Plotkin for semigroup varieties.
Keywords: semigroups, varieties, universal algebraic geometry. 
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     author = {A. N. Shevlyakov},
     title = {\large {Equationally} {Noetherian} varieties of semigroups and {B.~Plotkin's} problem},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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A. N. Shevlyakov. \large Equationally Noetherian varieties of semigroups and B.~Plotkin's problem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 724-734. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a3/