On the applicability to semirings of two theorems from the theory of rings and modules that a semiring S satisfies the Baer criterion and every
S-semimodule can be embedded in an injective
Direct sums of injective semimodules and direct products of projective semimodules over semirings the cardinality of
S. As a consequence, we obtain semiring analogs of well-known characterizations of classical
On semirings satisfying the Baer criterion respect to one-sided ideals of
S) semimodules satisfy the above condition. We propose a newmethod
On semirings whose simple semimodules are projective. In particular, we establish that for every semiring S this condition implies the injectivity of all simple
S