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2019 On finitely stable domains, I
Stefania Gabelli, Moshe Roitman
J. Commut. Algebra 11(1): 49-67 (2019). DOI: 10.1216/JCA-2019-11-1-49

Abstract

We prove that an integral domain $R$ is stable and one-dimensional if and only if $R$ is finitely stable and Mori. If $R$ satisfies these two equivalent conditions, then each overring of $R$ also satisfies these conditions, and it is $2$-$v$-generated. We also prove that, if $R$ is an Archimedean stable domain such that $R'$ is local, then $R$ is one-dimensional and so Mori.

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Stefania Gabelli. Moshe Roitman. "On finitely stable domains, I." J. Commut. Algebra 11 (1) 49 - 67, 2019. https://doi.org/10.1216/JCA-2019-11-1-49

Information

Published: 2019
First available in Project Euclid: 13 March 2019

zbMATH: 07037588
MathSciNet: MR3922425
Digital Object Identifier: 10.1216/JCA-2019-11-1-49

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

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.11 • No. 1 • 2019
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