Journal of Commutative Algebra

On finitely stable domains, I

Stefania Gabelli and Moshe Roitman

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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.

Article information

Source
J. Commut. Algebra, Volume 11, Number 1 (2019), 49-67.

Dates
First available in Project Euclid: 13 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.jca/1552464132

Digital Object Identifier
doi:10.1216/JCA-2019-11-1-49

Mathematical Reviews number (MathSciNet)
MR3922425

Zentralblatt MATH identifier
07037588

Subjects
Primary: 13A15: Ideals; multiplicative ideal theory
Secondary: 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 13G05.

Keywords
Archimedean domain finite character finitely stable Mori domain stable ideal

Citation

Gabelli, Stefania; Roitman, Moshe. On finitely stable domains, I. J. Commut. Algebra 11 (2019), no. 1, 49--67. doi:10.1216/JCA-2019-11-1-49. https://projecteuclid.org/euclid.jca/1552464132


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