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Mat. Zametki, 2008, Volume 83, Issue 4, Pages 536–544 (Mi mz4574)  

This article is cited in 10 scientific papers (total in 10 papers)

On the Applicability to Semirings of Two Theorems from the Theory of Rings and Modules

S. N. Il'in

Kazan State University

Abstract: Problems concerning the extension of the Baer criterion for injectivity and the embedding theorem of an arbitrary module over a ring into an injective module to the case of semirings are treated. It is proved that a semiring $S$ satisfies the Baer criterion and every $S$-semimodule can be embedded in an injective semimodule if and only if $S$ is a ring.

Keywords: Baer criterion for injectivity, embedding of modules, semiring, semimodule, semigroup, commutative monoid

DOI: https://doi.org/10.4213/mzm4574

Full text: PDF file (403 kB)
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English version:
Mathematical Notes, 2008, 83:4, 492–499

Bibliographic databases:

UDC: 512.552.35
Received: 12.03.2007
Revised: 03.09.2007

Citation: S. N. Il'in, “On the Applicability to Semirings of Two Theorems from the Theory of Rings and Modules”, Mat. Zametki, 83:4 (2008), 536–544; Math. Notes, 83:4 (2008), 492–499

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. M. Vechtomov, A. V. Cheraneva, “Semifields and their properties”, J. Math. Sci., 163:6 (2009), 625–661  mathnet  crossref  mathscinet  elib  elib
    2. Il'in S.N., Katsov Y., “On $p$-Schreier varieties of semimodules”, Comm. Algebra, 39:4 (2011), 1491–1501  crossref  mathscinet  zmath  isi  scopus
    3. Katsov Y., Nam T.G., “Morita Equivalence and Homological Characterization of Semirings”, J. Algebra. Appl., 10:3 (2011), 445–473  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. N. Abyzov, Yu. A. Alpin, N. A. Koreshkov, M. F. Nasrutdinov, S. N. Tronin, “Algebraicheskie issledovaniya v Kazanskom universitete ot V. V. Morozova do nashikh dnei”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 44–59  mathnet
    5. S. N. Il'in, “Semirings satisfying the Baer criterion”, Russian Math. (Iz. VUZ), 57:3 (2013), 26–31  mathnet  crossref
    6. Il'in S.N., Katsov Y., “On Serre's Problem on Projective Semimodules Over Polynomial Semirings”, Commun. Algebr., 42:9 (2014), 4021–4032  crossref  mathscinet  zmath  isi  scopus
    7. Il'in S.N., “On Projective Covers of Semimodules and Perfect Semirings”, J. Algebra. Appl., 13:6 (2014), 1450014  crossref  mathscinet  zmath  isi  scopus
    8. Abuhlail J.Y., “Some Remarks on Tensor Products and Flatness of Semimodules”, Semigr. Forum, 88:3 (2014), 732–738  crossref  mathscinet  zmath  isi  scopus
    9. Abuhlail J.Y. Il'in S.N. Katsov Y. Nam T.G., “on V-Semirings and Semirings All of Whose Cyclic Semimodules Are Injective”, Commun. Algebr., 43:11 (2015), 4632–4654  crossref  mathscinet  zmath  isi  elib  scopus
    10. Il'in S.N., Katsov Y., Nam T.G., “Toward homological structure theory of semimodules: On semirings all of whose cyclic semimodules are projective”, J. Algebra, 476 (2017), 238–266  crossref  mathscinet  zmath  isi  scopus
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