二维中心化子猜想
The two-dimensional Centralizer Conjecture
摘要：
一个由C. C.- A.郑俊雄Mckay和S. S.- S. Wang说：假设$A$和$B$的雅可比矩阵在$\mathbb{C}[x,y]$中是可逆的，并且对于$A,B,w \in \mathbb{C}[x,y]$，$A$和$w$的雅可比矩阵为零。然后是$w \in \mathbb{C}[A]$。我们证明了CMW的结果中$\mathbb{C}$可以用任何特征为零的域代替，并猜想了$D$上的二维中心化猜想：假设$A$和$B$的雅可比矩阵在$D[x,y]$中可逆，而$A$和$w$的雅可比矩阵对于$A,B,w \in D[x,y]$为零，则$D$是特征为零的整环.然后是$w \in D[A]$。我们证明了如果著名的二维雅可比猜想成立，那么二维中心化猜想也成立。
英文摘要：
A result by C. C.-A. Cheng, J. H. Mckay and S. S.-S. Wang says the following: Suppose the Jacobian of $A$ and $B$ is invertible in $\mathbb{C}[x,y]$ and the Jacobian of $A$ and $w$ is zero for $A,B,w \in \mathbb{C}[x,y]$. Then $w \in \mathbb{C}[A]$. We show that in CMW's result it is possible to replace $\mathbb{C}$ by any field of characteristic zero, and we conjecture the following 'two-dimensional Centralizer Conjecture over $D$': Suppose the Jacobian of $A$ and $B$ is invertible in $D[x,y]$ and the Jacobian of $A$ and $w$ is zero for $A,B,w \in D[x,y]$, $D$ is an integral domain of characteristic zero. Then $w \in D[A]$. We show that if the famous two-dimensional Jacobian Conjecture is true, then the two-dimensional Centralizer Conjecture is true.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
