The ghost dimension of a ring

Hovey, Mark; Lockridge, Keir

doi:10.1090/S0002-9939-09-09672-5

The ghost dimension of a ring
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by Mark Hovey and Keir Lockridge PDF

Proc. Amer. Math. Soc. 137 (2009), 1907-1913 Request permission

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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