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The ghost dimension of a ring

Author(s): Mark Hovey; Keir Lockridge
Journal: Proc. Amer. Math. Soc. 137 (2009), 1907-1913.
MSC (2000): Primary 16E10; Secondary 18G20, 13D05, 55P43
Posted: January 15, 2009
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Abstract | References | Similar articles | Additional information

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$.

References:

[CCM08]
Sunil K. Chebolu, J. Daniel Christensen, and Ján Minác, Ghosts in modular representation theory, Adv. Math. 217 (2008), 2782-2799. MR 2397466 (2008m:20018)

[Chr98]
J. Daniel Christensen, Ideals in triangulated categories: Phantoms, ghosts and skeleta, Adv. Math. 136 (1998), no. 2, 284-339. MR 1626856 (99g:18007)

[HLP07]
Mark Hovey, Keir Lockridge, and Gena Puninski, The generating hypothesis in the derived category of a ring, Math. Z. 256 (2007), no. 4, 789-800. MR 2308891

[Lam99]
T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, 1999. MR 1653294 (99i:16001)

[Loc06]
Keir H. Lockridge, The generating hypothesis in general stable homotopy categories, Ph.D. thesis, University of Washington, 2006.

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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: 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
Posted: January 15, 2009
Communicated by: Birge Huisgen-Zimmermann
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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