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Algebra Logika, 2020, Volume 59, Number 2, Pages 155–168 (Mi al941)  

This article is cited in 1 scientific paper (total in 1 paper)

Primitive normality and primitive connectedness of the class of injective $S$-acts

E. L. Efremov

Far Eastern Federal University, Vladivostok

Abstract: The paper deals monoids over which the class of all injective $S$-acts is primitive normal and primitive connected. The following results are proved: the class of all injective acts over any monoid is primitive normal; the class of all injective acts over a right reversible monoid $S$ is primitive connected iff $S$ is a group; if a monoid $S$ is not a group and the class of all injective acts is primitive connected, then a maximal (w.r.t. inclusion) proper subact of $ _SS$ is not finitely generated.

Keywords: monoid, $S$-act, injective $S$-act, primitive normal theory, primitive connected theory.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00531_а
Ministry of Science and Higher Education of the Russian Federation 075-02-2020-1482-1
(E. L. Efremov) Supported by RFBR (project No. 17-01-00531) and by RF Ministry of Education and Science (Suppl. Agreement No. 075-02-2020-1482-1 of 21.04.2020).


DOI: https://doi.org/10.33048/alglog.2020.59.201

Full text: PDF file (233 kB)
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English version:
Algebra and Logic, 2020, 59:2, 103–113

Bibliographic databases:

UDC: 510.67:512.56
Received: 25.02.2019
Revised: 14.07.2020

Citation: E. L. Efremov, “Primitive normality and primitive connectedness of the class of injective $S$-acts”, Algebra Logika, 59:2 (2020), 155–168; Algebra and Logic, 59:2 (2020), 103–113

Citation in format AMSBIB
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\paper Primitive normality and primitive connectedness of the class of injective $S$-acts
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\yr 2020
\vol 59
\issue 2
\pages 155--168
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\crossref{https://doi.org/10.33048/alglog.2020.59.201}
\transl
\jour Algebra and Logic
\yr 2020
\vol 59
\issue 2
\pages 103--113
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Stepanova, E. L. Efremov, “Primitivnaya normalnost klassa slabo in'ektivnykh poligonov”, Sib. matem. zhurn., 62:3 (2021), 640–658  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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