论文标题
注入性模块的扭转和弱的序列序列
Torsion of injective modules and weakly pro-regular sequences
论文作者
论文摘要
令$ r $ a换成戒指，$ \ mathfrak {a} \ subset r $理想，$ i $ a Imptive $ r $ -module和$ s \ s \ subset r $ a多上封闭的集合。 When $R$ is Noetherian it is well-known that the $\mathfrak{a}$-torsion sub-module $Γ_{\mathfrak{a}}(I)$, the factor module $I/Γ_{\mathfrak{a}}(I)$ and the localization $I_S$ are again injective $R$-modules.我们通过相对的概念来调查这些属性，以$ \ mathfrak {a} $ - 注射$ r $ -modules。特别是，我们从相对注入的模块方面获得了弱促序序列的另一种表征。另外，我们还介绍了非诺瑟式通勤环$ r $和注射$ r $ $模型的示例，以前的属性不存在。此外，在某些弱的促性条件下，我们获得了Mayer-Vietoris类型的结果。
Let $R$ a commutative ring, $\mathfrak{a} \subset R$ an ideal, $I$ an injective $R$-module and $S \subset R$ a multiplicatively closed set. When $R$ is Noetherian it is well-known that the $\mathfrak{a}$-torsion sub-module $Γ_{\mathfrak{a}}(I)$, the factor module $I/Γ_{\mathfrak{a}}(I)$ and the localization $I_S$ are again injective $R$-modules. We investigate these properties in the case of a commutative ring $R$ by means of a notion of relatively-$\mathfrak{a}$-injective $R$-modules. In particular we get another characterization of weakly pro-regular sequences in terms of relatively injective modules. Also we present examples of non-Noetherian commutative rings $R$ and injective $R$-modules for which the previous properties do not hold. Moreover, under some weak pro-regularity conditions we obtain results of Mayer-Vietoris type.
