On the number of terms in the middle of almost split sequences over cycle-finite artin algebras

TL;DR

This paper proves that in the module category of a cycle-finite artin algebra, the middle of an almost split sequence contains at most five terms, providing a bound on the complexity of these sequences.

Contribution

It establishes a universal upper bound of five terms for the middle of almost split sequences in cycle-finite artin algebras, a new result in representation theory.

Findings

The number of middle terms in almost split sequences is at most 5.

Provides a bound applicable to all cycle-finite artin algebras.

Enhances understanding of the structure of almost split sequences.

Abstract

We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.