素理想(p)在Q(μ^(1\3^m))中的分解

Decomposition of prime ideal(p) in Q(μ^(1/3^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 3m 次根扩张Q (μ13m ) (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 13 m ) has been discussed and solved completely.