The ghost dimension of a ring

Mark Hovey 
Wesleyan University   
mhovey@wesleyan.edu   

Keir Lockridge
Wake Forest University
lockrikh@wfu.edu

We introduce the concept of the ghost dimension 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 the ghost dimension of R is less than or equal to the weak
dimension of R, with equality if R is coherent or has weak dimension
1.