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

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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. 
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     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},
     publisher = {mathdoc},
     volume = {83},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a5/}
}
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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_a5/