摘要： The freeness of projective semimodules over k-local semirings is mainly studied. Firstly,some properties of local semirings are proposed. Then, an analogue for semirings of Nakayama's lemma is obtained. Furthermore, it is proved that finitely generated projective semimodules are free on k-local semirings.
Finally, suppose P is a finitely generated R-semimodule, then P is projective if and only if Pm is free for the subtractive maximal ideal m of R.