Representations of algebras as universal localizations

2002/05/31 by Amnon Neeman, Andrew Ranicki, Aidan Schofield · 1 citation
Mathematics · #math.RA #msc:16A08 #msc:18E35

paper · pdf

published as Math. Proc. Camb. Phil. Soc. 136, 105-117 (2004) · v2 (minor revision of v1). 15 pages, LATEX, to be published in the Mathematical Proceedings of the Cambridge Philosophical Society

arxiv created 2002/07/02 · arxiv updated 2009/11/30

Abstract

Every finitely presented algebra S is shown to be Morita equivalent to the universal localization σ^-1R 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^-1R,σ^-1R) 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^-1R.

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