On finitely stable domains
Commutative Algebra
2020-07-01 v4
Abstract
We study Archimedean and locally Archimedean stable domains. We prove that a domain is stable and one-dimensional if and only if it is finitely stable and Mori. But we give examples of Archimedean stable local domains that are not one-dimensional. We also prove that a locally Archimedean stable domain satisfies accp and that Archimedean stable semilocal domains are locally Archimedean. But generally, neither Archimedean stable domains, nor Archimedean semilocal domains are necessarily locally Archimedean.
Cite
@article{arxiv.1403.1394,
title = {On finitely stable domains},
author = {Stefania Gabelli and Moshe Roitman},
journal= {arXiv preprint arXiv:1403.1394},
year = {2020}
}
Comments
The new version corresponds to the published version, which is divided into two parts, and contains a simplified proof