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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 2, Pages 277–290 (Mi smj2305)  
This article is cited in 11 scientific papers (total in 11 papers)

$V$-semirings

S. N. Il'in

Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kazan
Full-text PDF (345 kB) Citations (11)
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Abstract: We investigate the semirings over which all simple semimodules are injective. In ring and module theory, the rings with an analogous condition are called $V$-rings. Therefore it is natural to call the semirings under consideration $V$-semirings. We obtain the semiring analogs of some well-known results on $V$-rings, including an analog of Kaplansky's theorem on commutative $V$-rings.
Keywords: simple semimodule, injective semimodule, essential extension, $V$-ring.
Received: 15.03.2011
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 2, Pages 222–231
DOI: https://doi.org/10.1134/S003744661202005X
Bibliographic databases:
Document Type: Article
UDC: 512.558
Language: Russian
Citation: S. N. Il'in, “$V$-semirings”, Sibirsk. Mat. Zh., 53:2 (2012), 277–290; Siberian Math. J., 53:2 (2012), 222–231
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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