Vol. 49, No. 1, 1973

Download this article
Download this article. For screen
For printing
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
Three theorems on imbedded prime divisors of principal ideals

Louis Jackson Ratliff, Jr.

Vol. 49 (1973), No. 1, 199–210

Let B be a finitely generated integral domain over a Noetherian domain A. The first theorem shows that there are only finitely many imbedded prime divisors of principal ideals in B if and only if this holds in A. The second theorem gives a necessary and sufficient condition in order that only finitely many height one prime ideals in A ramify in B, when A is locally factorial. The third theorem characterizes local domains which contain infinitely many imbedded prime divisors of principal ideals.

Mathematical Subject Classification 2000
Primary: 13G05
Received: 5 July 1972
Published: 1 November 1973
Louis Jackson Ratliff, Jr.