Hilbert-Speiser number fields and Stickelberger ideals

对于固定的素数p和整数n，当指数除p^n的任何阿贝尔扩张N/F关于p-整数环有正规基时，我们称数域F满足Hilbert-Speiser条件A(p^n)。在一定的Stickelberger理想下，我们给出了F满足A(p^n)的一个条件。

For a fixed prime number p and an integer n, we say that a number field F satisfies the Hilbert-Speiser condition A(p^n) when any abelian extension N/F of exponent dividing p^n has a normal basis with respect to the rings of p-integers. We gave a condition for F to satisfy A(p^n) in terms of a certain Stickelberger ideal.