Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 1 (2016), 101-118.

Completions of reduced local rings with prescribed minimal prime ideals

Susan Loepp and Byron Perpetua

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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.

Article information

Involve, Volume 9, Number 1 (2016), 101-118.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13B35: Completion [See also 13J10] 13F25: Formal power series rings [See also 13J05] 13J05: Power series rings [See also 13F25] 13J10: Complete rings, completion [See also 13B35]

completions of local rings minimal prime ideals


Loepp, Susan; Perpetua, Byron. Completions of reduced local rings with prescribed minimal prime ideals. Involve 9 (2016), no. 1, 101--118. doi:10.2140/involve.2016.9.101.

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