The ghost dimension of a ring

Abstract

We introduce the concept of the ghost dimension gh.dim.  R R of a ring R 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 ≤ R\leq gh.dim.  R R with equality if R R is coherent or w.dim.  R = 1 R=1 .