On the degree of irreducible morphisms

CLAUDIA CHAIO; MARIA INES PLATZECK; SONIA TREPODE

JOURNAL OF ALGEBRA

Elsevier

Año: 2004 vol. 281 p. 200 - 224

0021-8693

We study the degree of irreducible morphisms in generalized standard convex components of theAuslander–Reiten quiver of an artin algebra with the property that paths with the same origin and end vertices have equal length.We call the components with this last property components with length. In particular, we give two criteria to determine wether the degree of such an irreducible morphism f is finite or infinite. One of them is given in terms of the compositions of f with non-zero maps between modules in the component. The other states that the left degree of an irreducible map f is finite if and only if Kerf belongs to the component. We apply our results to irreducible morphisms over artin algebras of finite representation type and over tame hereditary algebras.