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 $n$ 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 $\Re ^{n+1}$.
