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2017 Factoring ideals and stability in integral domains
A. Mimouni
J. Commut. Algebra 9(2): 263-290 (2017). DOI: 10.1216/JCA-2017-9-2-263

Abstract

In an integral domain $R$, a nonzero ideal is called a \textit {weakly $ES$-stable ideal} if it can be factored into a product of an invertible ideal and an idempotent ideal of $R$; and $R$ is called a \textit {weakly $ES$-stable domain} if every nonzero ideal is a weakly $ES$-stable ideal. This paper studies the notion of weakly $ES$-stability in various contexts of integral domains such as Noetherian and Mori domains, valuation and Pr\"ufer domains, pullbacks and more. In particular, we establish strong connections between this notion and well-known stability conditions, namely, Lipman, Sally-Vasconcelos and Eakin-Sathaye stabilities.

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A. Mimouni. "Factoring ideals and stability in integral domains." J. Commut. Algebra 9 (2) 263 - 290, 2017. https://doi.org/10.1216/JCA-2017-9-2-263

Information

Published: 2017
First available in Project Euclid: 3 June 2017

zbMATH: 1370.13004
MathSciNet: MR3659951
Digital Object Identifier: 10.1216/JCA-2017-9-2-263

Subjects:
Primary: 13A15 , 13F05 , 13G05
Secondary: 13F30 , 13G05

Keywords: idempotent ideal , Invertible ideal , Noetherian domain , Prüfer domain , Pullbacks , strongly stable ideal , Valuation domain , weakly $ES$-stable domains , weakly $ES$-stable ideals

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.9 • No. 2 • 2017
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