  Let R be a commutative Noetherian local ring. We show that R is Gorenstein if
and only if every finitely generated R-module can be embedded in a finitely
generated R-module of finite projective dimension. This extends a result of
Auslander and Bridger to rings of higher Krull dimension, and it also improves
a result due to Foxby where the ring is assumed to be Cohen-Macaulay.
