Journal of Commutative Algebra
- J. Commut. Algebra
- Volume 11, Number 1 (2019), 49-67.
On finitely stable domains, I
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.
J. Commut. Algebra, Volume 11, Number 1 (2019), 49-67.
First available in Project Euclid: 13 March 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13A15: Ideals; multiplicative ideal theory
Secondary: 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 13G05.
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