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

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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

S

$S$ satisfies the Baer criterion and every

S

$S$ -semimodule can be embedded in an injective semimodule if and only if

S

$S$ 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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Linking options:

https://www.mathnet.ru/eng/mzm4574

https://doi.org/10.4213/mzm4574

https://www.mathnet.ru/eng/mzm/v83/i4/p536

This publication is cited in the following 13 articles:

Abuhlail J., Noegraha R.G., “Injective Semimodulos-Revisited”, J. Algebra. Appl., 21:01 (2022), 2250242
Katsov Y., “Axiomatizability of Homological Classes of Semimodules Over Semirings”, J. Algebra. Appl., 19:10 (2020), 2050182
S. N. Il'in, “On homological classification of semirings”, J. Math. Sci. (N. Y.), 256:2 (2021), 125–142
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
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
Il'in S.N., Katsov Y., “On Serre's Problem on Projective Semimodules Over Polynomial Semirings”, Commun. Algebr., 42:9 (2014), 4021–4032
Il'in S.N., “On Projective Covers of Semimodules and Perfect Semirings”, J. Algebra. Appl., 13:6 (2014), 1450014
Abuhlail J.Y., “Some Remarks on Tensor Products and Flatness of Semimodules”, Semigr. Forum, 88:3 (2014), 732–738
S. N. Il'in, “Semirings satisfying the Baer criterion”, Russian Math. (Iz. VUZ), 57:3 (2013), 26–31
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
Il'in S.N., Katsov Y., “On $p$ -Schreier varieties of semimodules”, Comm. Algebra, 39:4 (2011), 1491–1501
Katsov Y., Nam T.G., “Morita Equivalence and Homological Characterization of Semirings”, J. Algebra. Appl., 10:3 (2011), 445–473
E. M. Vechtomov, A. V. Cheraneva, “Semifields and their properties”, J. Math. Sci., 163:6 (2009), 625–661

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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