ABSTRACT
We show that if is a valuation domain with
a GCD domain, then
must be of rank one with value group either
or
. But we give an example of a rank-one valuation domain
with value group
for which
is not a GCD domain.
ACKNOWLEDGMENTS
The second-named author was supported by the Brain Korea 21 project in 2001. The third-named author's work was supported by the Post-doctoral Fellowship Program of the Korea Science & Engineering Foundation (KOSEF).