Geodesic
On the Applicability to Semirings of Two Theorems from the Theory of Rings and Modules
Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 536-544

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
S. N. Il'in. On the Applicability to Semirings of Two Theorems from the Theory of Rings and Modules. Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 536-544. http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a4/
@article{MZM_2008_83_4_a4,
     author = {S. N. Il'in},
     title = {On the {Applicability} to {Semirings} of {Two} {Theorems} from the {Theory} of {Rings} and {Modules}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {536--544},
     year = {2008},
     volume = {83},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a4/}
}
TY  - JOUR
AU  - S. N. Il'in
TI  - On the Applicability to Semirings of Two Theorems from the Theory of Rings and Modules
JO  - Matematičeskie zametki
PY  - 2008
SP  - 536
EP  - 544
VL  - 83
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a4/
LA  - ru
ID  - MZM_2008_83_4_a4
ER  - 
%0 Journal Article
%A S. N. Il'in
%T On the Applicability to Semirings of Two Theorems from the Theory of Rings and Modules
%J Matematičeskie zametki
%D 2008
%P 536-544
%V 83
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a4/
%G ru
%F MZM_2008_83_4_a4

[1] J. S. Golan, Semirings and Their Applications, Kluwer Acad. Publ., Dordrecht, 1999 | MR | Zbl

[2] R. Godeman, Algebraicheskaya topologiya i teoriya puchkov, IL, M., 1961 | MR | Zbl

[3] H. Wang, “Injective hulls of semimodules over additively-idempotent semirings”, Semigroup Forum, 48:1 (1994), 377–379 | DOI | MR | Zbl

[4] Y. Katsov, “Tensor products and injective envelopes of semimodules over additive regular semirings”, Algebra Colloq., 4:2 (1997), 121–131 | MR | Zbl

[5] S. S. Goncharov, Schetnye bulevy algebry i razreshimost, Nauchnaya kniga, Novosibirsk, 1996 | MR | Zbl