Morphisms represented by monomorphisms with n-torsionfree cokernel

TL;DR

This paper introduces a new class of morphisms related to monomorphisms with n-torsionfree cokernels, extending existing theorems and unifying results on torsionfreeness and Ext module grades.

Contribution

It defines and studies morphisms with n-torsionfree cokernels, generalizing and extending key theorems by Kato, Auslander, and Bridger.

Findings

Extended Kato's theorem on monomorphism-represented morphisms

Unified several results relating torsionfreeness and Ext grades

Provided new insights into morphisms with n-torsionfree cokernels

Abstract

We introduce and study a new class of morphisms which includes morphisms represented by monomorphisms in the sense of Auslander and Bridger. As an application, we give not only an extension of Kato's theorem on morphisms represented by monomorphisms, but also a common generalization of several results due to Auslander and Bridger that describe relationships between torsionfreeness and the grades of Ext modules.