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

  • Written by  Volodymydr Prokip
  • 1 comment


Volodymyr Prokip

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






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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An important generalization of the previously known the classical result

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