Vol. 107, No. 2, 1983

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
Powers of ideals in locally unmixed Noetherian rings

Louis Jackson Ratliff, Jr.

Vol. 107 (1983), No. 2, 459–472

It is known that the following statements are equivalent for a semi-local ring R: (1) R is analytically unramified; (2) There exists an open ideal I in R and an integer n 0 such that (In+i)a Ii for all i 1, where (In+i)a is the integral closure of In+i. Moreover, if R is analytically unramified and I is any ideal in R, then (2) holds for I and, (3) There exists an integer m 1 such that, with B = (Im)a, (Bi)a = Bi for all i 1. The main result in this paper shows that an analogous theorem holds with reduced unmixed local ring and I[i] replacing analytically unramified semi-local ring and (Ii)a, respectively, where I[i] is the intersection of certain primary ideals related to Ii. An application and a generalization are included.

Mathematical Subject Classification 2000
Primary: 13C15
Secondary: 13A15, 13J10
Received: 18 September 1981
Revised: 4 June 1982
Published: 1 August 1983
Louis Jackson Ratliff, Jr.