On Uniserial Modules in the Auslander-Reiten Quiver

TL;DR

This paper investigates irreducible maps involving finite-dimensional uniserial modules over associative algebras, classifying such maps over triangular algebras and estimating middle terms in almost split sequences.

Contribution

It provides a classification of irreducible maps between uniserial modules and estimates the middle terms in almost split sequences with uniserial end terms.

Findings

Classified irreducible maps between uniserial modules over triangular algebras.

Provided bounds for the number of middle terms in almost split sequences.

Enhanced understanding of the structure of uniserial modules in the Auslander-Reiten quiver.

Abstract

This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular algebras, and give estimates for the number of middle terms of an almost split sequence with a uniserial end term.