Abstract
Given A an artin algebra we study when the non-zero composition of four irreducible morphisms between indecomposable A-modules belongs to the fifth power of the radical of its module category. In particular, when A is a finite dimensional algebra over an algebraically closed field we prove that if the composition of four irreducible morphisms between indecomposable A-modules belongs to the fifth power of the radical of their module category then any composition of four irreducible morphisms between the same indecomposable A-modules so is.
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The authors thankfully acknowledge partial support from CONICET and from Universidad Nacional de Mar del Plata, Argentina. The first author is a researcher from CONICET.
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Presented by: Christof Geiss
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Chaio, C., Llodra-Schat, N. On the Composition of Four Irreducible Morphisms in the Fifth Power of the Radical. Algebr Represent Theor 24, 231–251 (2021). https://doi.org/10.1007/s10468-019-09942-z
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DOI: https://doi.org/10.1007/s10468-019-09942-z