素理想在Q(μ^(1/5))中的分解

Decomposition of Prime Ideal in Q(μ 1/5 )

设Ｑ为有理数域，令φ为由素数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），本文讨论了Ｐ在Ｑ的五次根扩张Ｑ（μ１５）（μ∈Ｒ）中的分解问题．并完全确定了分解所可能具有的形式（（ｐ，５）＝１）．

Assumption: Q is the field of ratonal number, φ is p adic valuation of Q, R is the valuation ring with respect to φ, and p is the prime ideal with respect to R . On the basis of these, the question of prime ideal decomposition in Q(μ 1/5 ) has been discussed (μ∈ R ). The possible type of decomposition of prime ideal has been established when (p ,5) equals to l.