关于余倾斜双模的k-挠自由模

k-Torsionfree Modules with Respect to Cotilting Modules

中文关键词:  余倾斜双模  $\omega$-$k$-挠自由模.

英文关键词:cotilting bimodules  $\omega$-$k$-torsionfree modules.

中文摘要:

      文章通过对余倾斜双模~$_\Lambda \omega_\Gamma$的讨论, 给出有限生成左~$\Lambda$-模是~$\omega$-$k$-挠自由模的一个充要条件, 并讨论了~$T_\omega^i$ 的扩张封闭问题.特别地, 本文得到了一些左内射维数~$\leq k$ 的余倾斜双模~$_\Lambda\omega_\Gamma$ 的一些性质.

英文摘要:

      Let $\Lambda$ and $\Gamma$ be left and right Noetherian rings and $_\Lambda \omega_\Gamma$ a cotilting bimodule. A necessary and sufficient condition for a finitely generated $\Lambda$-module to be $\omega$-$k$-torsionfree is given and the extension closure of $T_\omega^i$ is discussed. As applications, we give some results of $_\Lambda \omega_\Gamma$ related to $l.{\rm id}(\omega)\leq k$.