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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

On LPI rings

Najib Mahdou
Rachida El Khalfaoui
Abdeslam Mimouni
Pages
784–792
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we extend the $LPI$ property (that is, every locally principal ideal in an integral domain is invertible) to rings with zero-divisors and we study the class of commutative rings in which every regular locally principal ideal is invertible called $LPI$ rings.
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Key Findings & Data:We investigate the stability of this property under homomorphic image, and its transfer to various contexts of constructions such as direct products, amalgamation of rings and trivial ring extensions.
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Conclusion & Impact:Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Locally principal ideals · regular ideals · trivial extension

Abstract

In this paper, we extend the $LPI$ property (that is, every locally principal ideal in an integral domain is invertible) to rings with zero-divisors and we study the class of commutative rings in which every regular locally principal ideal is invertible called $LPI$ rings. We investigate the stability of this property under homomorphic image, and its transfer to various contexts of constructions such as direct products, amalgamation of rings and trivial ring extensions. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

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Cite This Article

Mahdou, N., Khalfaoui, R. E., Mimouni, A. (2022). On LPI rings. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 784–792. https://ajindex.com/articles/529640

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