Geodesic
Direct products of modules and the pure semisimplicity conjecture. Part II
Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 317-321

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DOI

We prove that the module categories of Noether algebras (i.e., algebras module finite over a noetherian center) and affine noetherian PI algebras over a field enjoy the following product property: whenever a direct product \prod _(n \in N) M_n of finitely generated indecomposable modules M_n is a direct sum of finitely generated objects, there are repeats among the isomorphism types of the M_n. The rings with this property satisfy the pure semisimplicity conjecture which stipulates that vanishing one-sided pure global dimension entails finite representation type. 
Huisgen-Zimmermann, Birge; Saorín, Manuel. Direct products of modules and the pure semisimplicity conjecture. Part II. Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 317-321. doi: 10.1017/S001708950202013X
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     title = {Direct products of modules and the pure semisimplicity conjecture. {Part} {II}},
     journal = {Glasgow mathematical journal},
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     year = {2002},
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     doi = {10.1017/S001708950202013X},
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