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

Irwing Kaplansky

A stable range of class full matrices over elementary divisor ring

 

 

Bohdana Kuznitska

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv

 
 

Abstract:

 

Theorem 1. Let R be a commutative Bezout ring a stable range 2. Let A, B∈ F(R2) be such that AR2+BR2=R2, moreover, the matrix B admits a diagonal reduction. Then there exists a full matrix T∈ F(R2) such that A+BT  is an invertible matrix.

Theorem 2. Let R be a commutative elementary divisor ring. If A, B F(R2) and AR2+BR2=R2, then there exists full matrix T F(R2) such that A+BT  is an invertible matrix.

 

 

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Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
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