Elementary Reduction of Matrices over Right 2-Euclidean Rings

• Date: 2004
• Main Authors: Romaniv, A. M., Романів, О. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3879
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We introduce a concept of noncommutative (right) 2-Euclidean ring. We prove that a 2-Euclidean ring is a right Hermite ring, a right Bezout ring, and a GE n -ring. It is shown that an arbitrary right unimodular string of length not less than 3 over a right Bezout ring of stable rank possesses an el...