Abstract
Problems concerning the extension of the Baer criterion for injectivity and 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.
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Original Russian Text © S. N. Il’in, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 4, pp. 536–544.
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Il’in, S.N. On the applicability to semirings of two theorems from the theory of rings and modules. Math Notes 83, 492–499 (2008). https://doi.org/10.1134/S000143460803022X
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DOI: https://doi.org/10.1134/S000143460803022X