Nil-quasi-clean companion matrices
Let \(R\) be a ring with identity. An element \(e\) in \(R\) is called a quasi-idempotent element if \(e^2=ke\) for some central unit \(k\) in \(R\). For an element \(b\) in \(R\), if there is a positive integer \(m\) such that \(b^m=0\), then \(b\) is called a nilpotent element of \(R\). An elemen...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2026
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2466 |
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| Journal Title: | Algebra and Discrete Mathematics |
| Download file: |  |
Institution
Algebra and Discrete Mathematics| Summary: | Let \(R\) be a ring with identity. An element \(e\) in \(R\) is called a quasi-idempotent element if \(e^2=ke\) for some central unit \(k\) in \(R\). For an element \(b\) in \(R\), if there is a positive integer \(m\) such that \(b^m=0\), then \(b\) is called a nilpotent element of \(R\). An element \(r\) in \(R\) is called a nil-quasi-clean element if \(r\) is a sum of a quasi-idempotent and a nilpotent. If every element of \(R\) is nil-quasi-clean, then \(R\) is called a nil-quasi-clean ring. This paper completely determines nil-quasi-clean companion matrices over a field. |
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| DOI: | 10.12958/adm2466 |