Sep 192013
 

\[K=\Bbb Q(\sqrt2,\sqrt3,\sqrt5,\dotsc,\sqrt{p_n},\dotsc),\]

这里 \(p_n\) 表示第 \(n\) 个质数, \(n=1,2,\dotsc\). 容易说明, \(K/\Bbb Q\) 是代数扩张.

现在我们关心的是, \(K/\Bbb Q\) 是无限扩张吗? 直觉告诉我们, 答案是肯定的! 如何证明?

有点难度, 远远不是看上去那么简单.

 Posted by at 8:25 am

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