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

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.