Algebras of Bounded Finite Dimensional Representation Type

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Abstract (in LaTex)

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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