根扩张中的素分解律

The Prime Ideal Decomposition Law in k(μ 1m )

设ｋ为域，ｋ的特征为零，φ为ｋ的秩为１的非平凡，非阿基米德赋值，ｒ为与其相对应的赋值环，Ｐ为ｒ的极大理想．本文讨论了Ｐ在ｋ的根扩张ｋ（μ１ｍ）（μ∈ｒ，ｍ为正整数）中的素理想Ｐ的分解律问题及其与Ｐ在ｋ（ζｍ）（ζｍ为ｍ次本原单位根）中的任意扩张Ｐ在ｋ（μ１ｍ。

Assume k is a field, and Its character is zero, Φ is a valuation of rank 1, non-trivial, non-ARCHIMEDEAN of k. r is the valuation ring of Φ. p is the maximal ideal of r. In this Paper, we have discussed the problem of prime ideal decomposition law in k(μ 1m ). Any p of the extension of p in k(ζ m) decomposes in k(μ 1m ,ζ m) and the relationship of them.