On the compositions of irreducible morphisms

C. CHAIO

Guanajuato

Congreso; IV ARTA; 2015

CIMAT

We consider A to be an artin algebra. By modA we mean the category of finitely generated leftA-modules.One of the aims of the Representation theory of artin algebras is to study the compositions ofirreducible morphisms and their relationship with the powers of the radical of their modulecategory.As we know, the composition of n irreducible morphisms between indecomposable modulescould be a non-zero map in the (n+1)-th power of the radical of its module category. In [CPT], fora finite dimensional algebra over an algebraically closed field, the authors studied thecomposition of irreducible morphisms between modules in regular components of theAuslander-Reiten quiver.In this work, we generalize to the context of artin algebras the results proven in [CPT]. We alsoobtain some useful consequences.