Presentations of rings with non-trivial semidualizing modules

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

Research output: Research - peer-reviewArticle

  • 7 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.

LanguageEnglish (US)
Pages165-180
Number of pages16
JournalCollectanea Mathematica
Volume63
Issue number2
DOIs
StatePublished - May 2012

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Ring
Module
Presentation
Gorenstein Ring
Homomorphic
Local Ring
If and only if
Cohen-Macaulay Ring
D-module
Cohen-Macaulay
Noetherian Ring
Finitely Generated
Expand
Decompose

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Presentations of rings with non-trivial semidualizing modules. / Jorgensen, David A.; Leuschke, Graham J.; Sather-Wagstaff, Sean.

In: Collectanea Mathematica, Vol. 63, No. 2, 05.2012, p. 165-180.

Research output: Research - peer-reviewArticle

Jorgensen DA, Leuschke GJ, Sather-Wagstaff S. Presentations of rings with non-trivial semidualizing modules. Collectanea Mathematica. 2012 May;63(2):165-180. Available from, DOI: 10.1007/s13348-010-0024-6
Jorgensen, David A. ; Leuschke, Graham J. ; Sather-Wagstaff, Sean. / Presentations of rings with non-trivial semidualizing modules. In: Collectanea Mathematica. 2012 ; Vol. 63, No. 2. pp. 165-180
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