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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 2, Pages 281–297
DOI: https://doi.org/10.17377/smzh.2017.58.204 (Mi smj2859) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On semirings whose simple semimodules are projective

S. N. Il'in

Kazan (Volga Region) Federal University, Lobachevskiĭ Institute of Mathematics and Mechanics, Kazan, Russia
Full-text PDF (377 kB) Citations (2)
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DOI: https://doi.org/10.17377/smzh.2017.58.204
Abstract: We study the semirings whose simple semimodules are all projective. In particular, we establish that for every semiring $S$ this condition implies the injectivity of all simple $S$-semimodules and show that, in contrast to the case of rings, the projectivity of all simple semimodules in general is not a left-right symmetric property.
Keywords: simple semimodule, projective semimodule, $V$-semiring, $V^*$-semiring.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.2045.2014
The author was supported by the subsidy of the Government Task for Kazan (Volga Region) Federal University (Grant 1.2045.2014).
Received: 23.04.2016
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 2, Pages 215–226
DOI: https://doi.org/10.1134/S0037446617020045
Bibliographic databases:
Document Type: Article
UDC: 512.558
MSC: 35R30
Language: Russian
Citation: S. N. Il'in, “On semirings whose simple semimodules are projective”, Sibirsk. Mat. Zh., 58:2 (2017), 281–297; Siberian Math. J., 58:2 (2017), 215–226
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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