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2016 Completions of reduced local rings with prescribed minimal prime ideals
Susan Loepp, Byron Perpetua
Involve 9(1): 101-118 (2016). DOI: 10.2140/involve.2016.9.101

Abstract

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.

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Susan Loepp. Byron Perpetua. "Completions of reduced local rings with prescribed minimal prime ideals." Involve 9 (1) 101 - 118, 2016. https://doi.org/10.2140/involve.2016.9.101

Information

Received: 21 August 2014; Revised: 27 October 2014; Accepted: 9 January 2015; Published: 2016
First available in Project Euclid: 22 November 2017

zbMATH: 06526328
MathSciNet: MR3438448
Digital Object Identifier: 10.2140/involve.2016.9.101

Subjects:
Primary: 13B35 , 13F25 , 13J05 , 13J10

Keywords: completions of local rings , minimal prime ideals

Rights: Copyright © 2016 Mathematical Sciences Publishers

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