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.
Citation
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
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