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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

Solvability of the system of matrix equations AX=B, XC=D over a principal ideal domain

 

Volodymyr Prokip

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

 

 

 

Abstract:

 

It is well know that the system of matrix equations AX=B, XC=D over a field F has a solution over F if and only if each of the equations AX = B and XC = D has a solution and AD = BC.

In this report we affirm that this criteria is true for the system of matrix equations AX=B, XC=D over a principal ideal domain.

 

 

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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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