Hilbert-Speiser number fields and Stickelberger ideals

对于固定素数p和整数n，当指数除以p^n的任意阿贝尔扩展n /F对p-整数环有正规基时，我们说数字域F满足Hilbert-Speiser条件a （p^n）。我们给出了F满足a （p^n）的条件用特定的stickkelberger理想来表示。

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.