Diagonalizability theorems for matrices over rings with finite stable range

• Date: 2018
• Main Author: Zabavsky, Bogdan
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: finite stable range; elementary divisor ring; Hermite ring; ring with elementary reduction of matrices; Bezout ring; minimal prime spectrum
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/923
• Journal Title: Algebra and Discrete Mathematics

We construct the theory of diagonalizability for matrices over Bezout ring with finite stable range. It is shown that every commutative Bezout ring with compact minimal prime spectrum is Hermite. It is also shown that a principal ideal domain with stable range 1 is Euclidean domain, and every semilo...