Isomorphism Problem For Uniserial Modules Over An Arbitrary Ring

TL;DR

This paper addresses the isomorphism problem for uniserial modules over arbitrary rings, providing partial solutions and methods, especially focusing on modules over quiver algebras, with implications for understanding module classification.

Contribution

It introduces new partial solutions and methods for the isomorphism problem of uniserial modules over arbitrary rings, including specific focus on quiver algebras.

Findings

Partial solution to the isomorphism problem using morphisms.

Method for partial classification based on submodule lattice assumptions.

Focus on uniserial modules over quiver algebras.

Abstract

Firstly, we give a partial solution to the isomorphism problem for uniserial modules of finite length with the help of the morphisms between these modules over an arbitrary ring. Later, under suitable assumptions on the lattice of the submodules, we give a method to partially solve the isomorphism problem for uniserial modules over an arbitrary ring. Particular attention is given to the natural class of uniserial modules defined over algebras given by quivers.