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December 2020 Structure of spectra of precompletions
Erica Barrett, Emil Graf, Susan Loepp, Kimball Strong, Sharon Zhang
Rocky Mountain J. Math. 50(6): 1965-1988 (December 2020). DOI: 10.1216/rmj.2020.50.1965

Abstract

Let T be a complete local (Noetherian) ring, and let A be a local subring of T such that the completion of A with respect to its maximal ideal is T. We investigate the possible structures of the partially ordered set Spec(A). Specifically, we explore the minimal prime ideals of A and their formal fibers, the maximal chains of prime ideals in A, and the number of prime ideals in A containing combinations of minimal prime ideals of A.

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Erica Barrett. Emil Graf. Susan Loepp. Kimball Strong. Sharon Zhang. "Structure of spectra of precompletions." Rocky Mountain J. Math. 50 (6) 1965 - 1988, December 2020. https://doi.org/10.1216/rmj.2020.50.1965

Information

Received: 14 November 2019; Revised: 11 May 2020; Accepted: 24 May 2020; Published: December 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/rmj.2020.50.1965

Subjects:
Primary: 13J10

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 6 • December 2020
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