Claims that artin algebras with representation bound at most four are exactly the wedged-string (bound three) and quadri-biserial (bound four) algebras, but the Kronecker algebra disproves the bound-four direction.
Auslander , ``Representation theory of artin algebras II", Comm
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Artin algebras of small representation bound
Claims that artin algebras with representation bound at most four are exactly the wedged-string (bound three) and quadri-biserial (bound four) algebras, but the Kronecker algebra disproves the bound-four direction.