Nil-quasi-clean companion matrices

• Date: 2026
• Main Authors: Su, Huadong, Liu, Shifeng
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2026
• Subjects: quasi-idempotent matrix; nil-quasi-clean; nilpotent matrix; finite field; 16U40; 15B33; 16S50
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2466
• Journal Title: Algebra and Discrete Mathematics

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...