素理想(p)在Q(μ^(1/25))中的分解

Decomposition of Prime Ideal (p) in Q(μ^(1/25))

设Q为有理数域 ,令 φ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 ) .用扩张平移的方法讨论了素理想 (p)在Q的 2 5次根扩张Q( μ1 2 5) ( μ∈R)中的分解问题 ,并完全解决了该问题 .

Let Q be the field of rational numbers,and φ be a p-adic valuation of Q,R be the valuation ring with respect to φ,(p) be the prime ideal with respect to R.In this paper,we use the method of translation of extension,and the problem of Law of decomposition of prime ideal (p) in Q(μ 125) has been discussed and solved completely.