论文标题
关于普通环的一些评论
Some remarks about normal rings
论文作者
论文摘要
我们给出一个建设性的证明，当$ r $正常时，$ r [x] $是正常的。我们将此结果应用于研究局部环的远程化所需的操作。我们的证明是基于$ r $没有零除数的情况，这比$ r $是一个积分域更重要的情况。我们必须使用一种建设性的解密技术，该技术通过合适的树中的合适的显式定位来代替最小素数（在经典数学中）的使用。
We give a constructive proof that $R[X]$ is normal when $R$ is normal. We apply this result to an operation needed for studying the henselization of a local ring. Our proof is based on the case where $R$ is without zero divisors, which is more involved than the case where $R$ is an integral domain. We have to use a constructive deciphering technique that replaces the use of minimal primes (in classical mathematics) by suitable explicit localizations in a suitable tree.
