n-T -torsionfree modules

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 introducedby Auslander and Bridger. We show that relative n-torsionfree modules have many similar properties of n-torsionfreemodules.