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Beyond totally reflexive modules and back

A survey on gorenstein dimensions
  • Lars Winther Christensen
  • Hans-Bjørn Foxby
  • Henrik Holm
Chapter

Abstract

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory’s connections with relative homological algebra and with studies of local ring homomorphisms. It ends close to the starting point: with a characterization of Gorenstein rings in terms of total acyclicity of complexes.

Keywords

Local Ring Projective Dimension Noetherian Ring Homological Dimension Dualizing Complex 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Lars Winther Christensen
    • 1
  • Hans-Bjørn Foxby
    • 2
  • Henrik Holm
    • 3
  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  2. 2.Department of Mathematical SciencesUniversity of CopenhagenKøbenhavn ØDenmark
  3. 3.Department of Basic Sciences and EnvironmentUniversity of CopenhagenFrederiksberg CDenmark

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