The composite of irreducible morphisms in regular components

CHAIO, CLAUDIA; PLATZECK, MARÍA INÉS; SONIA TREPODE

COLLOQUIUM MATHEMATICUM

Polish Academic of Sciences

Año: 2011 vol. 123 p. 27 - 47

0010-1354

We study when the composite of n irreducible morphisms between modules in a regular component of the Auslander-Reiten quiver is nonzero 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^infinite. 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.