论文标题
$ s $ -noetherian戒指和模块的扩展
An extension of $S$-noetherian rings and modules
论文作者
论文摘要
对于任何交换戒指$ a $，我们使用遗传性扭转理论$σ$而不是多重封闭的子集$ s \ subseteq {a} $引入了$ s $ noetherian戒指的概括。事实证明，如果$ a $是完全$σ$ -noetherian环，那么$σ$是有限类型的，而完全$σ$ -noetherian是本地财产。
For any commutative ring $A$ we introduce a generalization of $S$-noetherian rings using a hereditary torsion theory $σ$ instead of a multiplicatively closed subset $S\subseteq{A}$. It is proved that if $A$ is a totally $σ$-noetherian ring, then $σ$ is of finite type, and that totally $σ$-noetherian is a local property.
