Research demonstrates the isomorphism of projective covers in semimodules, implying traits of semirings are linked to their structure.
We show that every at semimodule having a projective cover coincides with that cover up to isomorphism. Also, we prove that all (finitely generated) semimodules over a semiring S are at iff S is a regular ring.
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Il'in et al. (2026) studied this question.
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