Journal of Commutative Algebra

Factoring ideals and stability in integral domains

A. Mimouni

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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.

Article information

J. Commut. Algebra, Volume 9, Number 2 (2017), 263-290.

First available in Project Euclid: 3 June 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13A15: Ideals; multiplicative ideal theory 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 13G05: Integral domains
Secondary: 13F30: Valuation rings [See also 13A18] 13G05: Integral domains

Invertible ideal idempotent ideal weakly $ES$-stable domains weakly $ES$-stable ideals strongly stable ideal valuation domain Prüfer domain Noetherian domain pullbacks


Mimouni, A. Factoring ideals and stability in integral domains. J. Commut. Algebra 9 (2017), no. 2, 263--290. doi:10.1216/JCA-2017-9-2-263.

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