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.
$n$-torsionfree modules, $n$-$T$-torsionfree module, $n$-spherical, $T$-grade
ZHANG, PEIYU and GENG, JIE
Turkish Journal of Mathematics: Vol. 43:
2, Article 9.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss2/9