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Spring 2020 The $p$-radical closure of local noetherian rings
Stefan Schröer
J. Commut. Algebra 12(1): 135-151 (Spring 2020). DOI: 10.1216/jca.2020.12.135

Abstract

Given a local noetherian ring R whose formal completion is integral, we introduce and study the p -radical closure R prc . Roughly speaking, this is the largest purely inseparable R -subalgebra inside the formal completion R ̂ . It turns out that the finitely generated intermediate rings R A R prc have rather peculiar properties. They can be used in a systematic way to provide examples of integral local rings whose normalization is nonfinite, that do not admit a resolution of singularities, and whose formal completion is nonreduced.

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Stefan Schröer. "The $p$-radical closure of local noetherian rings." J. Commut. Algebra 12 (1) 135 - 151, Spring 2020. https://doi.org/10.1216/jca.2020.12.135

Information

Received: 4 November 2016; Revised: 5 May 2017; Accepted: 15 May 2017; Published: Spring 2020
First available in Project Euclid: 13 May 2020

zbMATH: 07211331
MathSciNet: MR4097062
Digital Object Identifier: 10.1216/jca.2020.12.135

Subjects:
Primary: 13B22, 13F40, 13J10, 14JA05

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 1 • Spring 2020
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