Vol. 9, No. 1, 2016

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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