Vol. 9, No. 1, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 6, 901–1080
Issue 5, 721–899
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Other MSP Journals
Completions of reduced local rings with prescribed minimal prime ideals

Susan Loepp and Byron Perpetua

Vol. 9 (2016), No. 1, 101–118

Let T be a complete local ring of Krull dimension at least one, and let C1,C2,,Cm each be countable sets of prime ideals of T. We find necessary and sufficient conditions for T to be the completion of a reduced local ring A such that A has exactly m minimal prime ideals Q1,Q2,,Qm, and such that, for every i = 1,2,,m, the set of maximal elements of {P Spec(T)P A = Qi} is the set Ci.

completions of local rings, minimal prime ideals
Mathematical Subject Classification 2010
Primary: 13B35, 13F25, 13J05, 13J10
Received: 21 August 2014
Revised: 27 October 2014
Accepted: 9 January 2015
Published: 17 December 2015

Communicated by Scott T. Chapman
Susan Loepp
Department of Mathematics and Statistics
Williams College
18 Hoxsey Street
Bronfman Science Center
Williamstown, MA 01267
United States
Byron Perpetua
Department of Mathematics and Statistics
Williams College
c/o Susan Loepp, Bronfman Science Center
18 Hoxsey Street
Williamstown,MA 01267
United States