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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Similar characterization is obtained for T3(R) over a weak h-ring R.
📌 3 Key Takeaways
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Objective & Hypothesis:A ring R is strongly clean provided that for any a ∈ R, there exist an idempotent e ∈ R and a unit u ∈ R such that a = e + u and eu = ue.
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Key Findings & Data:Let T3(R) be a special subring of 3 by 3 matrix ring over R.
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Conclusion & Impact:Similar characterization is obtained for T3(R) over a weak h-ring R.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:strongly clean ring · matrix ring · local ring
Abstract
A ring R is strongly clean provided that for any a ∈ R, there exist an idempotent e ∈ R and a unit u ∈ R such that a = e + u and eu = ue. Let T3(R) be a special subring of 3 by 3 matrix ring over R. We prove, in this article, that T3(R) is strongly clean if and only if for any a ∈ J(R), b ∈ R, c ∈ 1 + J(R), either lb − ra or lb − rc is surjective. Similar characterization is obtained for T3(R) over a weak h-ring R.
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Cite This Article
Chen, H. (2011). A NOTE ON STRONGLY CLEAN MATRICES. International Electronic Journal of Algebra, Volume: 10 Issue: 10. https://ajindex.com/articles/1588269