  In this paper we generalize the theorem of Ein-Lazarsfeld-Smith (concerning
the behavior of symbolic powers of prime ideals in regular rings finitely
generated over a field of characteristic 0) to arbitrary regular rings
containing a field. The basic theorem states that in such rings, if P is a
prime ideal of height c, then for all n, the symbolic (cn)th power of P is
contained in the nth power of P. Results are also given in the non-regular
case: one must correct by a power of the Jacobian ideal in rings where the
Jacobian ideal is defined.
