On finitely stable domains, II

Stefania Gabelli, Moshe Roitman

Research output: Contribution to journalArticlepeer-review


Among other results, we prove the following: (1) A locally Archimedean stable domain satisfies accp. (2) A stable domain R is Archimedean if and only if every nonunit of R belongs to a height-one prime ideal of the integral closure R0 of R in its quotient field (this result is related to Ohm's theorem for Prufer domains). (3) An Archimedean stable domain R is one-dimensional if and only if R0 is equidimensional (generally, an Archimedean stable local domain is not necessarily one-dimensional). (4) An Archimedean finitely stable semilocal domain with stable maximal ideals is locally Archimedean, but generally, neither Archimedean stable domains, nor Archimedean semilocal domains are necessarily locally Archimedean.

Original languageEnglish
Pages (from-to)179-198
Number of pages20
JournalJournal of Commutative Algebra
Issue number2
StatePublished - 1 Jun 2020

Bibliographical note

Publisher Copyright:
© Rocky Mountain Mathematics Consortium.


  • Accp
  • Archimedean domain
  • Completely integrally closed
  • Finite character
  • Finitely stable
  • Locally archimedean
  • Mori domain
  • Stable ideal

ASJC Scopus subject areas

  • Algebra and Number Theory


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