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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

On common properties of Bezout domains and rings of matrices over them

 

Volodymyr Shchedryk

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

 

Abstract:

Theorem. Let R be a commutative Bezout domain in which for any three relatively prime nonzero elements a, b, c there exist such element r, that

(a+br,c)=1.

And let A1, A2, A3 be relatively prime on left side nonzero matrices from M2(R). Then there exist such matrix T and i,j,k {1,2,3}, that Ai+AjT, Ak are relatively prime on left side

 

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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
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Scientific seminar, Aprill, 2015