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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 724–734
DOI: https://doi.org/doi.org/10.33048/semi.2023.20.042
(Mi semr1605)
 

Mathematical logic, algebra and number theory

\large Equationally Noetherian varieties of semigroups and B. Plotkin's problem

A. N. Shevlyakov

Sobolev Institute of Mathematics, Pevtsova st. 13, 644099, Omsk, Russia
References:
Abstract: 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.
Funding agency Grant number
Russian Science Foundation 22-11-20019
The work is supported by RSF (grant 22-11-20019).
Received August 5, 2022, published September 22, 2023
Document Type: Article
UDC: 512.572
MSC: 20M07
Language: English
Citation: A. N. Shevlyakov, “\large Equationally Noetherian varieties of semigroups and B. Plotkin's problem”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 724–734
Citation in format AMSBIB
\Bibitem{She23}
\by A.~N.~Shevlyakov
\paper \large Equationally Noetherian varieties of semigroups and B.~Plotkin's problem
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 724--734
\mathnet{http://mi.mathnet.ru/semr1605}
\crossref{https://doi.org/doi.org/10.33048/semi.2023.20.042}
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