The composite of irreducible morphisms in regular components

Claudia Chaio, María Inés Platzeck, and Sonia Trepode. "The composite of irreducible morphisms in regular components." Colloquium Mathematicae 123.1 (2011): 27-47. <http://eudml.org/doc/283486>.

@article{ClaudiaChaio2011,
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 ℜ of the module category. We prove that in this case such a composite belongs to $ℜ^\{∞\}$. 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 $ℜ^\{n+1\}$.},
author = {Claudia Chaio, María Inés Platzeck, Sonia Trepode},
journal = {Colloquium Mathematicae},
keywords = {Artin algebras; Auslander-Reiten quivers; irreducible morphisms; almost sectional paths; indecomposable modules; Auslander-Reiten translations; almost-split sequences; infinite radical; regular components},
language = {eng},
number = {1},
pages = {27-47},
title = {The composite of irreducible morphisms in regular components},
url = {http://eudml.org/doc/283486},
volume = {123},
year = {2011},
}

TY - JOUR
AU - Claudia Chaio
AU - María Inés Platzeck
AU - Sonia Trepode
TI - The composite of irreducible morphisms in regular components
JO - Colloquium Mathematicae
PY - 2011
VL - 123
IS - 1
SP - 27
EP - 47
AB - 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 $ℜ^{∞}$. 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 $ℜ^{n+1}$.
LA - eng
KW - Artin algebras; Auslander-Reiten quivers; irreducible morphisms; almost sectional paths; indecomposable modules; Auslander-Reiten translations; almost-split sequences; infinite radical; regular components
UR - http://eudml.org/doc/283486
ER -