Presentations of rings with non-trivial semidualizing modules

David A. Jorgensen, Graham J. Leuschke, Sean Sather-Wagstaff

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Let R be a commutative noetherian local ring. A finitely generated R-module C is semidualizing if it is self-orthogonal and Hom R(C,C) ≅R. We prove that a Cohen-Macaulay ring R with dualizing module D admits a semidualizing module C satisfying R ≇ C ≇ D if and only if it is a homomorphic image of a Gorenstein ring in which the defining ideal decomposes in a cohomologically independent way. This expands on a well-known result of Foxby, Reiten and Sharp saying that R admits a dualizing module if and only if R is Cohen-Macaulay and a homomorphic image of a local Gorenstein ring.

Original languageEnglish (US)
Pages (from-to)165-180
Number of pages16
JournalCollectanea Mathematica
Volume63
Issue number2
DOIs
StatePublished - May 2012

Keywords

  • Gorenstein rings
  • Self-orthogonal modules
  • Semidualizing modules
  • Tate Ext
  • Tate Tor
  • Tor-independence

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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