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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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/

[1] A.H. Clifford, G.B. Preston, The The algebraic theory of semigroups, v. I, AMS, Providence, 1961 | MR | Zbl

[2] E. Daniyarova, A. Myasnikov, V. Remeslennikov, “Algebraic geometry over algebraic structures, II: Fundations”, J. Math. Sci., New York, 185:3 (2012), 389–416 | DOI | MR | Zbl

[3] T. Harju, J. Karhumäki, W. Plandowski, “Compactness of systems of equations in semigroups”, Automata, languages and programming, 22nd international colloquium, ICALP '95, Proceedings (Szeged, Hungary, July 10-14, 1995), LNCS, 944, eds. Fülöp Zoltán et al., Springer, Berlin, 1995, 444–454 | DOI | MR | Zbl

[4] T. Harju, J. Karhumäki, M. Petrich, “Compactness of systems of equations on completely regular semigroups”, Structures in logic and computer science, A selection of essays in honor of Andrzej Ehrenfeucht, LNCS, 1261, eds. Mycielski Jan et al.,, Springer, Berlin, 1997, 268–280 | DOI | Zbl

[5] B.I. Plotkin, “Problems in algebra inspired by universal algebraic geometry”, J. Math. Sci., New York, 139:4 (2006), 6780–6791 | DOI | MR | Zbl