Representations of algebras as universal localizations

Details Representations of algebras as universal localizations Representations of algebras as universal localizations

2002-05-03

arxiv.org/abs/math/0205034v2

Math. Proc. Camb. Phil. Soc. 136, 105-117 (2004)

Mathematics

Rings and Algebras

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

Scientific paper

Every finitely presented algebra S is shown to be Morita equivalent to the universal localization \sigma^{-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(\sigma^{-1}R,\sigma^{-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 \sigma^{-1}R.

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