n-T-torsionfree modules

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.