On finitely stable domains, I

Stefania Gabelli, Moshe Roitman

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)49-67
Number of pages19
JournalJournal of Commutative Algebra
Volume11
Issue number1
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 Rocky Mountain Mathematics Consortium.

Keywords

  • Archimedean domain
  • finite character
  • finitely stable
  • Mori domain
  • Stable ideal

ASJC Scopus subject areas

  • Algebra and Number Theory

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