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Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 3

Stability in Commutative Rings

Başak Ay SAYLAM
Pages
801–812
Publication Date
2020-05-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?

📌 3 Key Takeaways

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Objective & Hypothesis:Let R be a commutative ring with zero-divisors and I an ideal of R.
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Key Findings & Data:I is said to be ES-stable if JI = I 2 for some invertible ideal J ⊆ I , and I is said to be a weakly ES-stable ideal if there is an invertible fractional ideal J and an idempotent fractional ideal E of R such that I = JE .
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Conclusion & Impact:Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Weakly ES-stable rings · Prüfer rings · H-local rings

Abstract

Let R be a commutative ring with zero-divisors and I an ideal of R. I is said to be ES-stable if JI = I 2 for some invertible ideal J ⊆ I , and I is said to be a weakly ES-stable ideal if there is an invertible fractional ideal J and an idempotent fractional ideal E of R such that I = JE . We prove useful facts for weakly ES-stability and investigate this stability in Noetherian-like settings. Moreover, we discuss a question of A. Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?

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Cite This Article

SAYLAM, B. A. (2020). Stability in Commutative Rings. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 3, 801–812. https://ajindex.com/articles/193186

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