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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 3, Pages 640–658
DOI: https://doi.org/10.33048/smzh.2021.62.315 (Mi smj7584) 		 
The primitive normality of a class of weakly injective $S$-acts

A. A. Stepanova, E. L. Efremov

Far Eastern Federal University, School of Natural Sciences, FEFU campus, Russki Island, Russia
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DOI: https://doi.org/10.33048/smzh.2021.62.315
Abstract: The notion of weakly injective $S$-act can be regarded as a generalization of the notion of injective $S$-act. This article describes the finite monoids over which each weakly injective $S$-act has a primitively normal theory. Moreover, we show that the primitive normality of the class of all principally weakly injective $S$-acts is equivalent to $S$ being totally ordered.
Keywords: monoid, $S$-act, weakly injective $S$-act, primitive normal.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2020-1482-1
Russian Foundation for Basic Research 19-31-50021
A. A. Stepanova was supported by the Ministry of Science and Education of the Russian Federation (Agreement 075–02–2020–1482–1 of 21.04.2020). E. L. Efremov was supported by the Russian Foundation for Basic Research (Grant 19–31–50021).
Received: 08.04.2020
Revised: 26.01.2021
Accepted: 24.02.2021
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 3, Pages 521–536
DOI: https://doi.org/10.1134/S0037446621030150
Bibliographic databases:
Document Type: Article
UDC: 510.67:512.56
Language: Russian
Citation: A. A. Stepanova, E. L. Efremov, “The primitive normality of a class of weakly injective $S$-acts”, Sibirsk. Mat. Zh., 62:3 (2021), 640–658; Siberian Math. J., 62:3 (2021), 521–536
Citation in format AMSBIB
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\paper The primitive normality of a class of weakly injective $S$-acts
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\pages 640--658
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