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 .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-3,
author = {Claudia Chaio and Mar\'\i a In\'es Platzeck and Sonia Trepode},
title = {The composite of irreducible morphisms in regular components},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {27-47},
zbl = {1237.16017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-3}
}
Claudia Chaio; María Inés Platzeck; Sonia Trepode. The composite of irreducible morphisms in regular components. Colloquium Mathematicae, Tome 122 (2011) pp. 27-47. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-3/