English

Representations of algebras as universal localizations

Rings and Algebras 2007-05-23 v2

Abstract

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.

Keywords

Cite

@article{arxiv.math/0205034,
  title  = {Representations of algebras as universal localizations},
  author = {Amnon Neeman and Andrew Ranicki and Aidan Schofield},
  journal= {arXiv preprint arXiv:math/0205034},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T16:45:05.799Z