Abstract
We study the non-zero composition of n irreducible morphisms between modules in a regular component of the Auslander-Reiten quiver ΓA, lying in the n + 1-th power of the radical of a module category over an artin algebra. We apply such results to show that the composition of three irreducible morphisms between indecomposable modules cannot lie in ℜ4∖ℜ6.
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