The composite of irreducible morphisms in regular components
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 ℜ of the module category. We prove that in this case such a composite belongs to . 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 .