Vol. 60, No. 2, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
On Rees localities and Hi-local rings

Louis Jackson Ratliff, Jr.

Vol. 60 (1975), No. 2, 169–194

The main theorem gives a necessary and sufficient condition for each Rees locality = R[tb,u](M,tb,u) of a local ring (R,M) with respect to a principal ideal bR in R to be either an Hi-ring (that is, for all prime ideals p in such that height p = i, depth p = altitude ℒ− i) or a homogeneously Hi-ring (same condition holds for homogeneous p). Numerous corollaries follow concerning the cases: R is complete; R is Henselian; and, is Hi, for all i 0. A generalization to ideals generated by more than one element is given, and we relate the results to two of the chain conjectures on prime ideals.

Mathematical Subject Classification 2000
Primary: 13H10
Received: 16 October 1974
Published: 1 October 1975
Louis Jackson Ratliff, Jr.