The composite of irreducible morphisms
in regular components
Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 27-47
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $\Re $ of the module category. We prove that in this case such a composite belongs to $\Re ^{\infty }$. 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 $\Re ^{n+1}$.
Keywords:
study composite irreducible morphisms between modules regular component auslander reiten quiver non zero lies th power radical module category prove composite belongs infty apply these results characterize those string algebras having irreducible morphisms between band modules their composite non zero morphism
Affiliations des auteurs :
Claudia Chaio 1 ; María Inés Platzeck 2 ; Sonia Trepode 1
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author = {Claudia Chaio and Mar{\'\i}a In\'es Platzeck and Sonia Trepode},
title = {The composite of irreducible morphisms
in regular components},
journal = {Colloquium Mathematicum},
pages = {27--47},
publisher = {mathdoc},
volume = {123},
number = {1},
year = {2011},
doi = {10.4064/cm123-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm123-1-3/}
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Claudia Chaio; María Inés Platzeck; Sonia Trepode. The composite of irreducible morphisms in regular components. Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 27-47. doi: 10.4064/cm123-1-3
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