$n$-$T$-torsionfree modules
Authors : Peiyu Zhang, Jie Geng
Pages : 688-701
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :As a generalization of the Auslander-Reiten transpose, Xi introduced and studied a more general transpose, called the relative transpose (or, $T$-transpose). Based on this notion, the notion of relative $n$-torsionfree modules (or, $n$-$T$-torsionfree modules) is introduced in this paper, which is a generalization of the $n$-torsionfree modules introduced by Auslander and Bridger. We show that relative $n$-torsionfree modules have many similar properties of $n$-torsionfree modules.Keywords : $n$-torsionfree modules, $n$-$T$-torsionfree module, $n$-spherical, $T$-grade