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

Irwing Kaplansky

On some open Zabavsky’s problems


Andrij Romaniv

Department of Algebra
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
National Academy of Sciences of Ukraine



Theorem. Let R be an elementary divisor domain. If A, B relatively prime by left n×n matrices over R and matrix B is disappear then there exist matrix T such that

A+BT∈ GLn(R).


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