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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 3, Pages 33–39 (Mi ivm8780)  
This article is cited in 1 scientific paper (total in 1 paper)

Semirings satisfying the Baer criterion

S. N. Il'in

Chair of Algebra and Mathematical Logics, Kazan (Volga Region) Federal University, Kazan, Russia
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Abstract: It is well-known that for modules over rings the Baer injectivity criterion takes place. In this paper we prove that under one additional condition this criterion is also valid for modules over semirings. We prove that a semiring $S$ satisfies the Baer criterion if and only if all injective (with respect to one-sided ideals of $S$) semimodules satisfy the above condition. We propose a new method for constructing semirings satisfying the Baer criterion.
Keywords: semiring, injective semimodule, Baer criterion.
Received: 30.01.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 3, Pages 26–31
DOI: https://doi.org/10.3103/S1066369X13030031
Bibliographic databases:
Document Type: Article
UDC: 512.558
Language: Russian
Citation: S. N. Il'in, “Semirings satisfying the Baer criterion”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 3, 33–39; Russian Math. (Iz. VUZ), 57:3 (2013), 26–31
Citation in format AMSBIB
\Bibitem{Ili13}
\by S.~N.~Il'in
\paper Semirings satisfying the Baer criterion
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 3
\pages 33--39
\mathnet{http://mi.mathnet.ru/ivm8780}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 3
\pages 26--31
\crossref{https://doi.org/10.3103/S1066369X13030031}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84876221872}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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