The composite of irreducible morphisms in regular components
Volume 123 / 2011
Colloquium Mathematicum 123 (2011), 27-47
MSC: 16G70, 16G20, 16E10.
DOI: 10.4064/cm123-1-3
Abstract
We study when the composite of irreducible morphisms between modules in a regular component of the Auslander–Reiten quiver is non-zero and lies in the n+1-th power of the radical \Re of the module category. We prove that in this case such a composite belongs to \Re ^{\infty }. We apply these results to characterize those string algebras having n irreducible morphisms between band modules such that their composite is a non-zero morphism in \Re ^{n+1}.
