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Algebra i logika, 2022, Volume 61, Number 6, Pages 784–795
DOI: https://doi.org/10.33048/alglog.2022.61.607 (Mi al2742) 		 
Generalized stability of the class of injective $S$-acts

A. A. Stepanova

Far Eastern Federal University, Vladivostok
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DOI: https://doi.org/10.33048/alglog.2022.61.607
Abstract: The concept of $P$-stability is a particular case of generalized stability of complete theories. We study injective $S$-acts with a $P$-stable theory. It is proved that the class of injective $S$-acts is $(P,1)$-stable only if $S$ is a one-element monoid. Also we describe commutative and linearly ordered monoids $S$ the class of injective $S$-acts over which is $(P,s)$-, $(P,a)$-, and $(P,e)$-stable.
Keywords: monoid, act over monoid, injective act, generalized stability.
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: 04.03.2022
Revised: 13.10.2023
English version:
Algebra and Logic, 2022, Volume 61, Issue 6, Pages 537–544
DOI: https://doi.org/10.1007/s10469-023-09718-x
Document Type: Article
UDC: 510.67:512.56
Language: Russian
Citation: A. A. Stepanova, “Generalized stability of the class of injective $S$-acts”, Algebra Logika, 61:6 (2022), 784–795; Algebra and Logic, 61:6 (2022), 537–544
Citation in format AMSBIB
\Bibitem{Ste22}
\by A.~A.~Stepanova
\paper Generalized stability of the class of injective $S$-acts
\jour Algebra Logika
\yr 2022
\vol 61
\issue 6
\pages 784--795
\mathnet{http://mi.mathnet.ru/al2742}
\transl
\jour Algebra and Logic
\yr 2022
\vol 61
\issue 6
\pages 537--544
\crossref{https://doi.org/10.1007/s10469-023-09718-x}
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    		Алгебра и логика Algebra and Logic
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