Direct products of modules and the pure semisimplicity conjecture

It is shown that, if R is either an Artin algebra or a commutative noetherian domain of Krull dimension 1, then infinite direct products of R-modules resist direct sum decomposition as follows: If (M-n)(n is an element ofN) is a family of non-isomorphic, finitely generated, indecomposable R-modules, then Pi (n is an element ofN) M-n is not a direct sum of finitely generated modules. The bearing of this direct product condition on the pure semisimplicity problem is discussed.