Abstract
Let Λ be an algebra over an algebraically closed field. We compare the partial order ≤ hom in the module category of Λ with a certain relation ≤ stab in the stable module category of Λ. Both relations coincide if Λ is hereditary. Starting with any non-hereditary representation-finite algebra Λ, we construct a representation-finite algebra Λ′, obtained by a covering of the Auslander-Reiten quiver of Λ, such that for Λ′ both relations do not coincide.
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