Geodesic
The composite of irreducible morphisms in regular components
Claudia Chaio 1   ; María Inés Platzeck 2   ; Sonia Trepode 1
1 Departamento de Matemática Facultad de Ciencias Exactas y Naturales Funes 3350 Universidad Nacional de Mar del Plata 7600 Mar del Plata, Argentina
2 Instituto de Matemática Universidad Nacional del Sur Av. Alem 1253 8000 Bahía Blanca, Argentina
Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 27-47 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\Re ^{n+1}$.
DOI : 10.4064/cm123-1-3
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

Claudia Chaio  1   ; María Inés Platzeck  2   ; Sonia Trepode  1

1 Departamento de Matemática Facultad de Ciencias Exactas y Naturales Funes 3350 Universidad Nacional de Mar del Plata 7600 Mar del Plata, Argentina
2 Instituto de Matemática Universidad Nacional del Sur Av. Alem 1253 8000 Bahía Blanca, Argentina 
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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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