素理想(p)在Q(μ^(1/5^m))中的分解

Decomposition of prime ideal (p) in Q(μ^(1/5^m)

设Q为有理数域,令为由奇素数p生成的有理数域Q的P-adic赋值。R为与其相对应的赋值环,(p)为R的极大理想(素理想)。本文用扩张平移的方法讨论了素理想(p)在Q的5m次根扩张Q(μ15m)(μ∈R)中的分解问题。

Let Q be the field of rational numbers,and  is a p-adic valuation of Q,R is the valuation ring with respect to ,(p)is the prime ideal with respect to R.In this paper,We use the method of translation of extension,and the problem of law of decomposion of prime ideal (p) in Q(μ15m) has been discussed and solved completely.