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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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Bezout rings of stable range 1.5

V. Shchedryk, 10 Apr, 2014

Bezout rings of stable range 1.5

Effective domain

B. Zabavsky, 14 Nov, 2013

Effective domain

Outdoor meeting of seminar

O. Romaniv, 29 May, 2015

Outdoor meeting of seminar

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Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
1 Universytetska Str., 79000 Lviv, Ukraine
Tel: (+380 322) 394 172
E-mail: oromaniv at franko.lviv.ua

Outdoor meeting, 27 May, 2016