Solvability Conditions for Mixed Sylvester Equations in Rings

Huaxi Chen, Long Wang, Qian Wang


This paper has been motivated by Wang and He [Q.W. Wang and Z.H. He, Solvability conditions and general solution for mixed Sylvester equations. Automatica, 49 (2013) 2713-2719] in which the authors consider some solvability conditions for mixed Sylvester matrix equations. The paper also considers the same problem in the setting of a regular ring. Using the purely algebraic technique, we present some necessary and sufficient conditions for the solvability to mixed Sylvester equations in rings.

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