On hereditary reducibility of 2-monomial matrices over commutative rings

• Date: 2019
• Main Authors: Bondarenko, Vitaliy M., Gildea, Joseph, Tylyshchak, Alexander A., Yurchenko, Natalia V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2019
• Subjects: commutative ring; Jacobson radical; 2-monomial matrix; hereditary reducible matrix; similarity; linear operator; free module; 15B33; 15A30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1333
• Journal Title: Algebra and Discrete Mathematics

A 2-monomial matrix over a commutative ring \(R\) is by definition any matrix of the form \(M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k&0\\0&tI_{n-k}\end{smallmatrix}\right)\), \(0<k<n\), where \(t\) is a non-invertible element of \(R\), \(\Phi\) the companion matrix to \...