Characterization of irreducible morphisms of degree three

Abstract

We characterize the irreducible morphisms of left (right) degree three in terms of configurations of almost split sequences in the category of finitely generated modules over a perfect field. Furthermore, most of the results obtained hold for artin algebras.

Keywords:

• Auslander–Reiten quiver
• irreducible
• degrees
• almost split sequences
• radical

2000 Mathematics Subject Classification:

• 16G70
• 16G20
• 16E10

Acknowledgments

The authors thankfully acknowledge partial support from CONICET and from Universidad Nacional de Mar del Plata, Argentina. The first author is a researcher from CONICET.

Disclosure statement

No potential conflict of interest was reported by the authors.