素理想在Q(μ^(1/3))中的分解

Decomposition of Prime Ideal in Q(μ13)Zhang Jinxia

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的三次根扩张Ｑ（μ１３）（μ∈Ｒ）中的分解律与Ｐ在Ｑ（ζ３）（ζ３为３次本原单位根）中的任一扩张Ｐ１在Ｑ（μ１３，ζ３）中的分解律的关系，从而在（ｐ，３）＝１时。

Assumption: Q is the field of rational 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. The relationship between the decomposition law of P in Q(μ13)(μ∈R) and that of P1 in Q(μ13·ζ3)(ζ3 is the third primitive unity root), Which is anyextension of P in Q(ζ3) was descussed. The problem of prime ideal decomposition in Q(μ13) is completely solved if (p,3) is equal to l.