Totally acyclic complexes and locally Gorenstein rings

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Abstract

A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every acyclic complex of injective modules is totally acyclic. We extend this characterization, which is due to Iyengar and Krause, to arbitrary commutative noetherian rings, i.e. we remove the assumption about a dualizing complex. In this context Gorenstein, of course, means locally Gorenstein at every prime.

Original languageEnglish
Article number1850039
JournalJournal of Algebra and its Applications
Volume17
Issue number3
DOIs
StatePublished - Mar 1 2018

Keywords

  • Gorenstein ring
  • totally acyclic complex

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