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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Marks, Frederik 2015. Universal localisations and tilting modules for finite dimensional algebras. Journal of Pure and Applied Algebra, Vol. 219, Issue. 7, p. 3053.

    Angeleri Hügel, Lidia Koenig, Steffen and Liu, Qunhua 2012. On the uniqueness of stratifications of derived module categories. Journal of Algebra, Vol. 359, p. 120.

    Angeleri Hügel, Lidia Koenig, Steffen and Liu, Qunhua 2011. Recollements and tilting objects. Journal of Pure and Applied Algebra, Vol. 215, Issue. 4, p. 420.

    Keller, Bernhard and Van den Bergh, Michel 2011. Deformed Calabi–Yau completions. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2011, Issue. 654,

    Krause, Henning and Šťovíček, Jan 2010. The telescope conjecture for hereditary rings via Ext-orthogonal pairs. Advances in Mathematics, Vol. 225, Issue. 5, p. 2341.

    Ranicki, Andrew 2009. Noncommutative localization in algebraic L-theory. Advances in Mathematics, Vol. 220, Issue. 3, p. 894.

    Neeman, Amnon 2007. Noncommutative localisation in algebraic K-theory II. Advances in Mathematics, Vol. 213, Issue. 2, p. 785.

    Neeman, Amnon and Ranicki, Andrew 2004. Noncommutative localisation in algebraicK–theory I. Geometry & Topology, Vol. 8, Issue. 3, p. 1385.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 136, Issue 1
  • January 2004, pp. 105-117

Representations of algebras as universal localizations

  • DOI:
  • Published online: 01 January 2004

Given a presentation of a finitely presented group, there is a natural way to represent the group as the fundamental group of a 2-complex. The first part of this paper demonstrates one possible way to represent a finitely presented algebra $S$ in a similarly compact form. From a presentation of the algebra, we construct a quiver with relations whose path algebra is finite dimensional. When we adjoin inverses to some of the arrows in the quiver, we show that the path algebra of the new quiver with relations is $M_n(S)$ where $n$ is the number of vertices in our quiver. The slogan would be that every finitely presented algebra is Morita equivalent to a universal localization of a finite dimensional algebra.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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