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Journals / International Electronic Journal of Algebra / 2026 / Volume: 21 Issue: 21

WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS

Andrada Ciımpean
Peter Danchev
Pages
—
Publication Date
2017-01-17
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AI Summary & Key Takeaways

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

Algebra 15(2014), 145–156]

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce and study the weakly nil-clean index associated to a ring.
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Key Findings & Data:We also give some simple properties of this index and show that rings with the weakly nil-clean index 1 are precisely those rings that are abelian weakly nil-clean, thus showing that they coincide with uniquely weakly nil-clean rings.
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Conclusion & Impact:Algebra 15(2014), 145–156]
🔬Design:Research Article
📍Scope:2014 Verileri
⚙️Variables:: Nil-clean ring · uniquely nil-clean ring · weakly nil-clean ring

Abstract

We introduce and study the weakly nil-clean index associated to a ring. We also give some simple properties of this index and show that rings with the weakly nil-clean index 1 are precisely those rings that are abelian weakly nil-clean, thus showing that they coincide with uniquely weakly nil-clean rings. Next, we define certain types of nilpotent elements and weakly nil-clean decompositions by obtaining some results when the weakly nil-clean index is at most 2 and, moreover, we somewhat characterize rings with weakly nil-clean index 2. After that, we compute the weakly nil-clean index for T2(Zp), T3(Zp) and M2(Z3), respectively, as well as we establish a result on the weakly nilclean index of Mn(R) whenever R is a ring. Our results considerably extend and correct the corresponding ones from [Int. Electron. J. Algebra 15(2014), 145–156]

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Cite This Article

Ciımpean, A., Danchev, P. (2017). WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS. International Electronic Journal of Algebra, Volume: 21 Issue: 21. https://doi.org/10.24330/ieja.296326

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