Stickelberger’s theorem
Theorem 1 (Stickelberger).
Let be a cyclotomic field extension of with Galois group , and consider the group ring . Define the Stickelberger element by
and take such that as well. Then is an annihilator for the ideal class group of .
Note that itself need not be an annihilator, just that any multiple of it in is.
This result allows for the most basic between the (otherwise hard to determine) of a cyclotomic ideal class group and its of annihilators. For an application of Stickelberger’s theorem, see Herbrand’s theorem.
Title | Stickelberger’s theorem |
---|---|
Canonical name | StickelbergersTheorem |
Date of creation | 2013-03-22 14:12:31 |
Last modified on | 2013-03-22 14:12:31 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 6 |
Author | mathcam (2727) |
Entry type | Theorem |
Classification | msc 11R29 |
Defines | Stickelberger element |