Indecomposable and irreducible \(t\)-monomial matrices over commutative rings

• Date: 2016
• Main Authors: Bondarenko, Vitaliy Mykhaylovych, Bortos, Maria, Dinis, Ruslana, Tylyshchak, Alexander
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: local ring; similarity; indecomposable matrix; irreducible matrix; canonically \(t\)-cyclic matrix; defining sequence; group; representation; 15B33; 15A30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/287
• Journal Title: Algebra and Discrete Mathematics

We introduce the notion of the defining  sequence of a permutation  indecomposable  monomial matrix over a commutative ring and obtain   necessary conditions for such matrices to be indecomposable or irreducible in terms of this sequence.