k-Torsionfree Modules with Respect to Cotilting Modules
Received:December 07, 2006  Revised:October 30, 2007
Key Word: cotilting bimodules   $\omega$-$k$-torsionfree modules.
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 Author Name Affiliation ZHAO Zhi Bing School of Mathematics and Computational Science, Anhui University, Anhui 230039, China DU Xian Neng School of Mathematics and Computational Science, Anhui University, Anhui 230039, China
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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 $l.{\rm id}(\omega)\leq k$.