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Summer 2020 On finitely stable domains, II
Stefania Gabelli, Moshe Roitman
J. Commut. Algebra 12(2): 179-198 (Summer 2020). DOI: 10.1216/jca.2020.12.179

Abstract

Among other results, we prove the following:

  1. A locally Archimedean stable domain satisfies accp.

  2. A stable domain R is Archimedean if and only if every nonunit of R belongs to a height-one prime ideal of the integral closure R of R in its quotient field (this result is related to Ohm’s theorem for Prüfer domains).

  3. An Archimedean stable domain R is one-dimensional if and only if R is equidimensional (generally, an Archimedean stable local domain is not necessarily one-dimensional).

  4. An Archimedean finitely stable semilocal domain with stable maximal ideals is locally Archimedean, but generally, neither Archimedean stable domains, nor Archimedean semilocal domains are necessarily locally Archimedean.

Citation

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Stefania Gabelli. Moshe Roitman. "On finitely stable domains, II." J. Commut. Algebra 12 (2) 179 - 198, Summer 2020. https://doi.org/10.1216/jca.2020.12.179

Information

Received: 23 October 2016; Revised: 6 August 2017; Accepted: 13 August 2017; Published: Summer 2020
First available in Project Euclid: 2 June 2020

zbMATH: 07211334
MathSciNet: MR4105543
Digital Object Identifier: 10.1216/jca.2020.12.179

Subjects:
Primary: 13A15
Secondary: 13F05, 13G05

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 2 • Summer 2020
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