素数p在Q(^(2)(1/2)u)上的分解

Decomposition of Prime Ideal p over Q(^(2)(1/2)u)

设Q为有理数域,F=Q(^(2)(1/2)u)(其中是奇素数,u∈N),OF为域F对应的代数整数环.运用局部域的方法彻底解决了任意素数p在代数整数环OF中的素理想的分解问题,并且完全确定素数p在OF中可能出现的素理想分解的具体形式.

Assume Q as the field of rational number, F = Q （21u） （ l is an odd prime number and u N）, OF is algebraic integer ring of the corresponding field F. In this paper,the problem of ideal decomposition of every prime number p in the algebraic integer ring OF has been completely solved by using the method of local field, and the possible specific type of decomposition of prime ideal p in OF has been completely determined.