关于多项式的函数复合
On function compositions that are polynomials
摘要：
对于多项式映射$\mathbf{f} : k^n \to k^m$（$k$ a域），我们研究了可以写成复合$g = h \circ \mathbf{f}$的多项式$g \in k[t_1,\ldots, t_n]$，其中$h: k^m \to k$是任意函数.在$k$是特征$0$的代数闭的且$\mathbf{f}$是满射的情况下，我们证明了$g = h \circ \mathbf{f}$蕴含$h$是多项式.
英文摘要：
For a polynomial map $\mathbf{f} : k^n \to k^m$ ($k$ a field), we investigate those polynomials $g \in k[t_1,\ldots, t_n]$ that can be written as a composition $g = h \circ \mathbf{f}$, where $h: k^m \to k$ is an arbitrary function. In the case that $k$ is algebraically closed of characteristic $0$ and $\mathbf{f}$ is surjective, we will show that $g = h \circ \mathbf{f}$ implies that $h$ is a polynomial.
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。
