论文标题
在雪瓦利的扩展定理上
On Chevalley's Extension Theorem
论文作者
论文摘要
丹尼尔·安德森（Daniel Anderson）教授最近告诉我，卡普兰斯基（Kaplansky）关于通勤戒指的书的定理56证明存在错误。他（Dan）的原因是“他（Kaplansky）通过反向纳入命令，但在最后一行使用包容性，因此我们不矛盾最大值（这是最小的）”。简短说明的目的是表明，虽然丹·安德森（Dan Anderson）在上述书籍的定理56证明中指出错误时似乎是正确的，但定理的陈述是Chevalley定理的正确结果。
Professor Daniel Anderson informed me, recently, that there is an error in the proof of Theorem 56 of Kaplansky's book on Commutative Rings. His (Dan's) reason was "He (Kaplansky) orders by reverse inclusion but in the last line uses inclusion, so we don't contradict maximality (which is minimality)". The aim of this short note is to indicate that while Dan Anderson appears to be correct in pointing out an error in the proof of Theorem 56 of the above mentioned book, the statement of the theorem is a correct consequence of a Theorem of Chevalley.
