论文标题
几乎krull尺寸零的平坦交换环型
Flat commutative ring epimorphisms of almost Krull dimension zero
论文作者
论文摘要
我们认为，u $ $ r \ to u $的平坦表现为$ i \ subset r $，其中$ iu = u $，商ring $ r/i $是krull dimension零的半落下。根据这些假设，我们表明$ r $ -MODULE $ U $的投影尺寸不超过$ 1 $。我们还描述了Geigle-lenzing垂直子类别$ u^{\ perp_ {0,1}} $ in $ r \ mathsf {-mod} $中的$。另外，假设环$ u $和所有戒指$ r/i $都是完美的，我们表明所有平坦的$ r $ $模型都是$ u $ - stronglonglongly flat。因此，我们获得了论文Arxiv：1801.04820的某些结果的概括，其中考虑了RING $ r $的本地化$ u = s^{ - 1} r $在乘法子集$ s \ subset r $上。
We consider flat epimorphisms of commutative rings $R\to U$ such that, for every ideal $I\subset R$ for which $IU=U$, the quotient ring $R/I$ is semilocal of Krull dimension zero. Under these assumptions, we show that the projective dimension of the $R$-module $U$ does not exceed $1$. We also describe the Geigle-Lenzing perpendicular subcategory $U^{\perp_{0,1}}$ in $R\mathsf{-Mod}$. Assuming additionally that the ring $U$ and all the rings $R/I$ are perfect, we show that all flat $R$-modules are $U$-strongly flat. Thus we obtain a generalization of some results of the paper arXiv:1801.04820, where the case of the localization $U=S^{-1}R$ of the ring $R$ at a multiplicative subset $S\subset R$ was considered.
