Indecomposables Live in All Smaller Lengths
نویسنده
چکیده
We show that there are no gaps in the lengths of the indecomposable objects in an abelian k-linear category over a field k provided all simples are absolutely simple. To derive this natural result we prove that any distributive minimal representation-infinite k-category is isomorphic to the linearization of the associated ray category which is shown to have an interval-finite universal cover with a free fundamental group so that the well-known theory of representation-finite algebras applies.
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