On T-Sylvester equations over commutative rings

Abstract In 1994, Wimmer showed the necessary and sufficient conditions for solvability of AX − X ⁎ B = C by means of Roth׳s criterion. It was shown that the equation over complex fields can be solved if and only if certain block matrices built from A , B and C are congruent. In this paper we extend the result to commutative rings with 2 invertible and show that it also holds for finite sets of matrices over a commutative ring with 2 invertible. We also discuss the solvability of X − AX T B = C over commutative rings with 2 invertible.