  A commutative local ring is generally defined to be a complete intersection
if its completion is isomorphic to the quotient of a regular local ring by an
ideal generated by a regular sequence. It has not previously been determined
whether or not such a ring is necessarily itself the quotient of a regular ring
by an ideal generated by a regular sequence. In this article, it is shown that
if a complete intersection is a one dimensional integral domain, then it is
such a quotient. However, an example is produced of a three dimensional
complete intersection domain which is not a homomorphic image of a regular
local ring, and so the property does not hold in general.
