论文标题
多项式环的典型延伸非常平坦
Étale extensions of polynomial rings are faithfully flat
论文作者
论文摘要
我们将OHI的标准应用于忠实的通勤环扩展，以证明任何étaleExtension $ k [y_1，\ ldots，y_n] \ subseteq k [x_1，\ ldots，x_n] $ comptation $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $特别是，如果$ k $是代数封闭的字段，则任何étale多项式映射$ k^{n} \ to k^{n} $是旋转的。
We apply Ohi's criterion for faithfully flatness of extensions of commutative rings to prove that any étale extension $k[Y_1, \ldots, Y_n]\subseteq k[X_1, \ldots, X_n]$ of polynomial rings (each in $n$ indeterminates) over a commutative ring $k$ is faithfully flat. In particular, if $k$ is an algebraically closed field then any étale polynomial map $k^{n} \to k^{n}$ is surjective.
