关于k-Local半环的一些结论

Some Results on k-Local Semirings

研究了k-local半环上投射半模的自由性问题.首先给出了local半环的一些性质.然后得到了半环上中山正引理的一种形式.进一步得到了,k-local半环上有限生成投射半模是自由的.最后,假设P是一个有限生成半模,则P投射当且仅当P_(m)自由,其中m是半环R的极大可减理想.

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 P_(m) is free for the subtractive maximal ideal m of R.