ABSTRACT
Let R be a domain with quotient field K, and let I be an ideal of R. We say that I is powerful (strongly primary) if whenever and
, we have
or
(
or
for some
). We show that an ideal with either of these properties is comparable to every prime ideal of R, that an ideal is strongly primary
it is a primary ideal in some valuation overring of R, and that R admits a powerful ideal
R admits a strongly primary ideal
R is conducive in the sense of Dobbs-Fedder. Finally, we study domains each of whose prime ideals is strongly primary.
ACKNOWLEDGMENTS
The second author acknowledges support from NATO Grant 970140.