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arXiv · 1407.2365

Direct products of modules and the pure semisimplicity conjecture. Part II

Birge Huisgen-Zimmermann·Manuel Saorín
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Abstract

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 $\prod_{n \in \Bbb N} M_n$ 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.

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Birge Huisgen-Zimmermann, Manuel Saorín. 2014-07-09. Direct products of modules and the pure semisimplicity conjecture. Part II. https://arxiv.org/abs/1407.2365

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