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

 

The ghost dimension of a ring


Authors: Mark Hovey and Keir Lockridge
Journal: Proc. Amer. Math. Soc. 137 (2009), 1907-1913
MSC (2000): Primary 16E10; Secondary 18G20, 13D05, 55P43
Published electronically: January 15, 2009
MathSciNet review: 2480270
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Abstract: We introduce the concept of the ghost dimension gh.dim. $ R$ of a ring $ R$. This is the longest nontrivial chain of maps in the derived category emanating from a perfect complex such that each map is zero on homology. We show that w.dim. $ R\leq$ gh.dim. $ R$ with equality if $ R$ is coherent or w.dim. $ R=1$.


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Additional Information

Mark Hovey
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: hovey@member.ams.org

Keir Lockridge
Affiliation: Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109
Email: lockrikh@wfu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09672-5
PII: S 0002-9939(09)09672-5
Received by editor(s): November 30, 2007
Received by editor(s) in revised form: June 10, 2008
Published electronically: January 15, 2009
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.