论文标题
扩展和扭转函子的coartinianess
Coartinianess of extension and torsion functors
论文作者
论文摘要
令$（R，\ Mathfrak {M}）$为$ \ Mathfrak {M} $ - ADIC拓扑，$ i $ $ r $的理想。 We investigate coartinianess of $\mathrm{Ext}$ and $\mathrm{Tor}$, show that the $R$-module $\mathrm{Ext}_{R}^{i}(N,M)$ is $I$-coartinian if $M$ is a linearly compact $I$-coartinian $R$-module and $N$ is an $ i $ -cofinite $ r $ - 尺寸最多$ 1 $; $ r $ -MODULE $ \ MATHRM {tor} _ {i}^{r}（n，m）$是$ i $ -coartinian，在这种情况下，$ m $是$ m $是线性紧凑的$ i $ i $ -coartinian，$ $ n $是二$ 2 $的，$ n $是有限生成的。
Let $(R,\mathfrak{m})$ be a commutative noetherian local ring with $\mathfrak{m}$-adic topology, $I$ an ideal of $R$. We investigate coartinianess of $\mathrm{Ext}$ and $\mathrm{Tor}$, show that the $R$-module $\mathrm{Ext}_{R}^{i}(N,M)$ is $I$-coartinian if $M$ is a linearly compact $I$-coartinian $R$-module and $N$ is an $I$-cofinite $R$-module of dimension at most $1$; the $R$-module $\mathrm{Tor}_{i}^{R}(N,M)$ is $I$-coartinian in the case $M$ is semi-discrete linearly compact $I$-coartinian and $N$ is finitely generated with dimension at most $2$.
