# Cycle-finite modules over artin algebras

## TL;DR

This paper investigates a specific class of modules over artin algebras, focusing on those not involved in cycles formed by homomorphisms from the infinite Jacobson radical, thereby advancing understanding of their representation theory.

## Contribution

It characterizes cycle-finite modules over artin algebras, providing new insights into their structure and the conditions under which they do not lie on certain cycles.

## Key findings

- Identification of modules not lying on cycles involving the infinite Jacobson radical
- Enhanced understanding of the structure of cycle-finite modules
- New criteria for classifying modules over artin algebras

## Abstract

We describe the representation theory of finitely generated indecomposable modules over artin algebras which do not lie on cycles of indecomposable modules involving homomorphisms from the infinite Jacobson radical of the module category.