论文信息 - The extension of Roth's theorem for matrix equations over a ring

The extension of Roth's theorem for matrix equations over a ring

Abstract This paper extends Roth's 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

Jianzhou Liu | Liping Huang

[1] W. Gustafson,et al. On matrix equivalence and matrix equations , 1979 .

[2] Paul M. Cohn,et al. Skew field constructions , 1973 .

[3] W. E. Roth,et al. The equations $AX-YB=C$ and $AX-XB=C$ in matrices , 1952 .

[4] Huang Liping,et al. The matrix equation AXB+CYD=Eover a simple artinian ring , 1995 .

[5] R. Guralnick. Roth's theorems and decomposition of modules , 1981 .

[6] J. K. Baksalary,et al. The matrix equation AXB+CYD=E , 1980 .

[7] R. Guralnick. Matrix equivalence and isomorphism of modules , 1982 .

[8] Harald K. Wimmer. The matrix equation X − AXB = C and an analogue of Roth's theorem , 1988 .

[9] Huang Liping. The matrix equation AXB−GXD = E over the quaternion field , 1996 .