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The composite of irreducible morphisms in regular components

Claudia Chaio; María Inés Platzeck; Sonia Trepode — 2011

Colloquium Mathematicae

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 $ℜ^{\infty}$ . 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 $ℜ^{n + 1}$ .

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