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

- Written by Volodymydr Prokip
- 1 comment

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Department of Algebra

Pidstryhach Institute for Applied Problems

of Mechanics and Mathematics

National Academy of Sciences of Ukraine

**Abstract:**

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*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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