南开大学学报(自然科学版) ›› 2021 ›› Issue (5): 21-.

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关于k-Local 半环的一些结论(英文)

  

  • 出版日期:2021-10-20 发布日期:2021-11-07

  • Online:2021-10-20 Published:2021-11-07

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.

关键词: local semiring, semimodule, ideal, localization