On sums of compositions of irreducible morphisms

C. CHAIO, NICOLÁS LLODRA SCHAT

Buenos Aires

Congreso; Congreso Latinoamericano de algebra; 2016

Universidad de Buenos Aires

We consider A an artin algebra, and mod A thecategory of finitely generated right A-modules.In this talk, we present some results about sums of compositions ofirreducible morphisms in mod A in relation with the powersof the radical of its module category.The notion of degree of an irreducible morphism, introduced by S.Liu played a fundamental role to obtain such results.In particular, for sums of compositions of irreducible morphisms oflength at most five, we get the following result.Theorem. Let A be an artin algebra and X,Y in ind A . Let n be an integer with 1< n