The extension of Rothʹs theorem for matrix equations over a ring Original Research Article

This paper extends Rothʹs similarity theorem as follows: Let R be a ring with identity, B(λ) = Σki = 0 Biλi ε Rm × q[λ]. If either R is a division ring and A ε Rn × n is algebraic, or R is finitely generated as a module over its center, then the matrix equation Σki = 0 AiXBi = C over R has a solution if and only if image