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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A test complex for Gorensteinness


Authors: Lars Winther Christensen and Oana Veliche
Journal: Proc. Amer. Math. Soc. 136 (2008), 479-487
MSC (2000): Primary 13H10, 13D25
Published electronically: November 6, 2007
MathSciNet review: 2358487
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ R$ be a commutative noetherian ring with a dualizing complex. By recent work of Iyengar and Krause (2006), the difference between the category of acyclic complexes and its subcategory of totally acyclic complexes measures how far $ R$ is from being Gorenstein. In particular, $ R$ is Gorenstein if and only if every acyclic complex is totally acyclic.

In this note we exhibit a specific acyclic complex with the property that it is totally acyclic if and only if $ R$ is Gorenstein.


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Additional Information

Lars Winther Christensen
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
Address at time of publication: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
Email: winther@math.unl.edu, lars.w.christensen@ttu.edu

Oana Veliche
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: oveliche@math.utah.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09129-0
PII: S 0002-9939(07)09129-0
Keywords: Gorenstein rings, dualizing complexes, totally acyclic complexes
Received by editor(s): July 14, 2006
Received by editor(s) in revised form: December 6, 2006, and January 17, 2007
Published electronically: November 6, 2007
Additional Notes: The first author was partly supported by a grant from the Carlsberg Foundation.
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.