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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
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.
Received August 5, 2022, published September 22, 2023
Citation:
A. N. Shevlyakov, “\large Equationally Noetherian varieties of semigroups and B. Plotkin's problem”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 724–734
Linking options:
https://www.mathnet.ru/eng/semr1605 https://www.mathnet.ru/eng/semr/v20/i2/p724
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Abstract page: | 36 | Full-text PDF : | 8 | References: | 8 |
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