#### Reduction matrices over Bezout rings

November 24, 2017 at 13:35 in Lecture Room 379

In particular, we will specify the necessary and sufficient conditions for a quasi-Euclidean duo-ring being a ring with elementary matrix reduction. Using this criterion we will be able to describe various duo-rings with elementary matrix reduction. Moreover, it will be established that any right Hermite stable range one ring is a right ω-Euclidean domain. Additionally, it will be proved that for any pair of nxn full matrices over elementary divisor ring, there exists a right (left) divisibility chain of length 2(n-1) and over PID – of length 2. Among the other results we will introduce the concept of e-atomic commutative domain...