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.