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Matematicheskie Zametki, 2008, Volume 83, Issue 4, Pages 536–544
DOI: https://doi.org/10.4213/mzm4574 (Mi mzm4574) 		 
This article is cited in 13 scientific papers (total in 13 papers)

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

S. N. Il'in

Kazan State University
Full-text PDF (403 kB) Citations (13)
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DOI: https://doi.org/10.4213/mzm4574
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 SS satisfies the Baer criterion and every SS-semimodule can be embedded in an injective semimodule if and only if SS is a ring.
Keywords: Baer criterion for injectivity, embedding of modules, semiring, semimodule, semigroup, commutative monoid.
Received: 12.03.2007
Revised: 03.09.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 4, Pages 492–499
DOI: https://doi.org/10.1134/S000143460803022X
Bibliographic databases:
UDC: 512.552.35
Language: Russian
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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    • This publication is cited in the following 13 articles:
    1. Abuhlail J., Noegraha R.G., “Injective Semimodulos-Revisited”, J. Algebra. Appl., 21:01 (2022), 2250242  crossref  mathscinet  isi
    2. Katsov Y., “Axiomatizability of Homological Classes of Semimodules Over Semirings”, J. Algebra. Appl., 19:10 (2020), 2050182  crossref  mathscinet  isi
    3. S. N. Il'in, “On homological classification of semirings”, J. Math. Sci. (N. Y.), 256:2 (2021), 125–142  mathnet  crossref  mathscinet
    4. 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
    5. 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
    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. S. N. Il'in, “Semirings satisfying the Baer criterion”, Russian Math. (Iz. VUZ), 57:3 (2013), 26–31  mathnet  crossref
    10. 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
    11. Il'in S.N., Katsov Y., “On pp-Schreier varieties of semimodules”, Comm. Algebra, 39:4 (2011), 1491–1501  crossref  mathscinet  zmath  isi  scopus
    12. 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
    13. E. M. Vechtomov, A. V. Cheraneva, “Semifields and their properties”, J. Math. Sci., 163:6 (2009), 625–661  mathnet  crossref  mathscinet  elib  elib
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