【摘要】 设F为代数数域,准为其秩为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(亦称为F中素理想,简称为素理想),本文用扩张平移的方法讨论了素理想P在域F的7次根扩张F(μ~1/7)(μ∈R)中的分解问题,并完全解决了该问题。更多还原

【Abstract】 Let F be the field of algebraic numbers,and φ be a non-trivial,non-archimedean valuation of F,R be the valuation ring with respect to φ,P be the prime ideal with respect to R.In this paper,We have used the method of translation of extension,and the problem of laws of decomposition of prime ideal in F(μ~1/7) has been discussed and been solved completely.更多还原