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.