On Gorenstein projective, injective and flat dimensions-A functorial description with applications

Lars Winther Christensen, Anders Frankild, Henrik Holm

Research output: Contribution to journalArticlepeer-review

241 Scopus citations

Abstract

Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical counterparts, these dimensions do not immediately come with practical and robust criteria for finiteness, not even over commutative noetherian local rings. In this paper we enlarge the class of rings known to admit good criteria for finiteness of Gorenstein dimensions: It now includes, for instance, the rings encountered in commutative algebraic geometry and, in the noncommutative realm, k-algebras with a dualizing complex.

Original languageEnglish
Pages (from-to)231-279
Number of pages49
JournalJournal of Algebra
Volume302
Issue number1
DOIs
StatePublished - Aug 1 2006

Keywords

  • Auslander categories
  • Bass formula
  • Chouinard formula
  • Dualizing complex
  • Foxby equivalence
  • Gorenstein flat dimension
  • Gorenstein injective dimension
  • Gorenstein projective dimension

Fingerprint

Dive into the research topics of 'On Gorenstein projective, injective and flat dimensions-A functorial description with applications'. Together they form a unique fingerprint.

Cite this