Representations of algebras as universal localizations

Neeman, Amnon; Ranicki, Andrew; Schofield, Aidan

Representations of algebras as universal localizations

Authors

Neeman, Amnon

Ranicki, Andrew

Schofield, Aidan

Description

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.
v2 (minor revision of v1). 15 pages, LATEX, to be published in the Mathematical Proceedings of the Cambridge Philosophical Society