English

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

R2 v1 2026-06-22T03:21:27.859Z