Vol. 91, No. 2, 1980

Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Integrally closed ideals and asymptotic prime divisors

Louis Jackson Ratliff, Jr.

Vol. 91 (1980), No. 2, 445–456

The first theorem characterizes local (Noetherian) domains that have a height one maximal ideal in their integral closure as those local domains whose maximal ideal M is a prime divisor (= associated prime) of the integral closure Ia of all nonzero ideals I contained in large powers of M. The second theorem describes (modulo a mild assumption) all local domains R that have the following property: for each ideal I in R and for all large n, all the ideals In and (In)a have the same prime divisors.

Mathematical Subject Classification 2000
Primary: 13A17, 13A17
Secondary: 13E05
Received: 29 August 1979
Published: 1 December 1980
Louis Jackson Ratliff, Jr.