The isomorphism problem for uniserial modules over an arbitrary ring

Abstract

First, we give a partial solution to the isomorphism problem for uniserial modules of finite length with the help of the morphisms between these modules. 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.

Keywords:

• Quivers
• representations
• uniform modules
• uniserial modules

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 16 D 10
• Secondary 16 G 20

Acknowledgments

The authors would like to thank the referee for his/her carefully reading the article and Prof. Dr. Toma Albu for his help.