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Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 5

NZI rings

Libin LI
Long WANG
Junchao WEI
Pages
781–792
Publication Date
2022-11-05
DOI
—
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AI Summary & Key Takeaways

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

Then R is a clean ring if and only if R is an exchange ring.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A ring R is called NZI if for any a \in R, l(a) is an N-ideal of R.
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Key Findings & Data:Next, we study the strong regularity of NZI rings and obtain the following results: (1) Let R be a left SF-ring.
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Conclusion & Impact:Then R is a clean ring if and only if R is an exchange ring.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Reduced ring · SF ring · strongly regular ring

Abstract

A ring R is called NZI if for any a \in R, l(a) is an N-ideal of R. In this paper, we first study some basic properties and basic extensions of NZI rings. Next, we study the strong regularity of NZI rings and obtain the following results: (1) Let R be a left SF-ring. Then R is a strongly regular ring if and only if R is an NZI ring; (2) If R is an NZI left MC2 ring and every simple singular left R-module is nil-injective, then R is reduced; (3) Let R be an NZI ring. Then R is a strongly regular ring if and only if R is a von Neumann regular ring; (4) Let R be an NZI ring. Then R is a clean ring if and only if R is an exchange ring.

Özet

A ring R is called NZI if for any a \in R, l(a) is an N-ideal of R. In this paper, we first study some basic properties and basic extensions of NZI rings. Next, we study the strong regularity of NZI rings and obtain the following results: (1) Let R be a left SF-ring. Then R is a strongly regular ring if and only if R is an NZI ring; (2) If R is an NZI left MC2 ring and every simple singular left R-module is nil-injective, then R is reduced; (3) Let R be an NZI ring. Then R is a strongly regular ring if and only if R is a von Neumann regular ring; (4) Let R be an NZI ring. Then R is a clean ring if and only if R is an exchange ring.

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Cite This Article

LI, L., WANG, L., WEI, J. (2022). NZI rings. Turkish Journal of Mathematics, Cilt: 37 - Sayı: 5, 781–792. https://ajindex.com/articles/608314

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