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[SUBn])[SUBn∈N] is a family of non-isomorphic, finitely generated, indecomposable R-modules, then ∏[SUBn∈N] M[SUBn] is not a direct sum of finitely generated modules. The bearing of this direct product condition on the pure semisimplicity problem is discussed. [ABSTRACT FROM AUTHOR]