A ring R is called weakly SG-hereditary if every ideal of R is SG-projective. In this note, we prove that a local domain R is a Noetherian Warfield domain if and only if it is weakly SG-hereditary. Furthermore, we prove that any countably generated submodule of any free module over a Noetherian local Warfield domain is SG-projective.

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关于本地弱SG遗传域的注释

甲环- [R被称为弱SG -hereditary如果每一个理想ř是SG -projective。在本文中，我们证明了当且仅当局部域R是弱SG世袭域时，它才是Noetherian Warfield域。此外，我们证明在Noetherian本地Warfield域上任何免费模块的任何可计数生成的子模块都是SG射影。