"I liked the algebraic way of looking at things.
I’m additionally fascinated when the algebraic method is applied to infinite objects”.

Irwing Kaplansky

The following report

Andrij Sagan

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...


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