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Representations of algebras as universal localizations

Amnon Neeman·Andrew Ranicki·Aidan Schofield
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Abstract

Every finitely presented algebra S is shown to be Morita equivalent to the universal localization σ^{-1}R of a finite dimensional algebra R. The construction provides many examples of universal localizations which are not stably flat, i.e. Tor^R_i(σ^{-1}R,σ^{-1}R) is non-zero for some i>0. It is also shown that there is no algorithm to determine if two Malcolmson normal forms represent the same element of σ^{-1}R.

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Amnon Neeman, Andrew Ranicki, Aidan Schofield. 2002-07-02. Representations of algebras as universal localizations. https://arxiv.org/abs/math/0205034

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