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Algebra i logika, 2023, Volume 62, Number 2, Pages 266–296
DOI: https://doi.org/10.33048/alglog.2023.62.206 (Mi al2760) 		 
Axiomatizability of the class of subdirectly irreducible $S$-acts over a commutative monoid

A. A. Stepanova, E. L. Efremov

Far Eastern Federal University, Vladivostok
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DOI: https://doi.org/10.33048/alglog.2023.62.206
Abstract: An axiomatizability criterion is found for the class of subdirectly irreducible $S$-acts over a commutative monoid. As a corollary, a number of properties are presented which a commutative monoid should satisfy provided that the class of subdirectly irreducible acts over it is axiomatizable. The question about a complete description of monoids over which the class of subdirectly irreducible acts is axiomatizable remains open even for the case of a commutative monoid.
Keywords: $S$-act, commutative monoid, subdirectly irreducible $S$-act, axiomatizable class.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2023-946
The work was carried out at Far Eastern Center for Mathematical Research and supported by RF Ministry of Education and Science, Agreement No. 075-02-2023-946 of 16.02.2023 on realization of Developmental Programs for Regional Scientific and Educational Mathematical Centers.
Received: 24.03.2022
Revised: 31.01.2024
English version:
Algebra and Logic, 2023, Volume 62, Issue 2, Pages 179–200
DOI: https://doi.org/10.1007/s10469-024-09735-4
Document Type: Article
UDC: 510.67:512.56
Language: Russian
Citation: A. A. Stepanova, E. L. Efremov, “Axiomatizability of the class of subdirectly irreducible $S$-acts over a commutative monoid”, Algebra Logika, 62:2 (2023), 266–296; Algebra and Logic, 62:2 (2023), 179–200
Citation in format AMSBIB
\Bibitem{SteEfr23}
\by A.~A.~Stepanova, E.~L.~Efremov
\paper Axiomatizability of the class of subdirectly irreducible $S$-acts over a commutative monoid
\jour Algebra Logika
\yr 2023
\vol 62
\issue 2
\pages 266--296
\mathnet{http://mi.mathnet.ru/al2760}
\transl
\jour Algebra and Logic
\yr 2023
\vol 62
\issue 2
\pages 179--200
\crossref{https://doi.org/10.1007/s10469-024-09735-4}
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