It is shown that for an arbitrary affine or noetherian algebra $R$ over a field, bounded representation type for the finite dimensional $R$-modules implies finite representation type for such modules. In fact, this boundedness assumption guarantees the existence of an ideal $I$ annihilating all finite dimensional $R$-modules such that $R/I$ is a finite dimensional algebra of finite representation type. Bounds on lengths of certain classes of finite-length modules are also investigated. For example, if $R$ is a noetherian ring satisfying the second layer condition and admitting a finite bound on the lengths of the indecomposable finite-length $R$-modules having co-artinian annihilators, it is proved that $R$ is a direct product of an artinian ring of finite representation type and a ring with no proper co-artinian ideals.
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