Classification of modules not lying on short chains

TL;DR

This paper characterizes finitely generated modules over artin algebras that are not part of short chains, utilizing injective and tilting modules over hereditary artin algebras for a comprehensive description.

Contribution

It provides a complete classification of modules not lying on short chains, connecting them with injective and tilting modules over hereditary algebras.

Findings

Complete description of modules not on short chains

Connection with injective and tilting modules

Framework applicable to finitely generated modules

Abstract

We give a complete description of finitely generated modules over artin algebras which are not the middle of a short chain of modules, using injective and tilting modules over hereditary artin algebras.