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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We prove that all trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$ are nil-clean and, up to similarity, that there are only two trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$.
📌 3 Key Takeaways
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Objective & Hypothesis:We prove that all trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$ are nil-clean and, up to similarity, that there are only two trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$.
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Key Findings & Data:We prove that all trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$ are nil-clean and, up to similarity, that there are only two trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$.
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Conclusion & Impact:We prove that all trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$ are nil-clean and, up to similarity, that there are only two trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:nil-clean · clean · similarity
Abstract
We prove that all trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$ are nil-clean and, up to similarity, that there are only two trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$.
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Cite This Article
Calugareanu, G. (2021). The nil-clean $2\times 2$ integral units. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 1. https://doi.org/10.15672/hujms.622655