On finitely stable domains, I

Stefania Gabelli; Moshe Roitman

doi:10.1216/JCA-2019-11-1-49

On finitely stable domains, I

Stefania Gabelli, Moshe Roitman

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	49-67
Number of pages	19
Journal	Journal of Commutative Algebra
Volume	11
Issue number	1
DOIs	https://doi.org/10.1216/JCA-2019-11-1-49
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019 Rocky Mountain Mathematics Consortium.

Keywords

Archimedean domain
Mori domain
Stable ideal
finite character
finitely stable

ASJC Scopus subject areas

Algebra and Number Theory

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10.1216/JCA-2019-11-1-49

Cite this

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KW - Mori domain

KW - Stable ideal

KW - finite character

KW - finitely stable

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On finitely stable domains, I

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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