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Stickelberger's theorem
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(Theorem)
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Note that  itself need not be an annihilator, just that any multiple of it in
![$ \mathbb{Z}[G]$](http://images.planetmath.org:8080/cache/objects/5642/l2h/img12.png "$ \mathbb{Z}[G]$") is.
This result allows for the most basic connections between the (otherwise hard to determine) structure of a cyclotomic ideal class group and its collection of annihilators. For an application of Stickelberger's theorem, see Herbrand's theorem.
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"Stickelberger's theorem" is owned by mathcam.
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(view preamble)
| Also defines: |
Stickelberger element |
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Cross-references: Herbrand's theorem, multiple, ideal class group, annihilator, group ring, Galois group, extension, cyclotomic field
There are 2 references to this entry.
This is version 3 of Stickelberger's theorem, born on 2004-02-27, modified 2004-03-02.
Object id is 5642, canonical name is StickelbergersTheorem.
Accessed 2575 times total.
Classification:
| AMS MSC: | 11R29 (Number theory :: Algebraic number theory: global fields :: Class numbers, class groups, discriminants) |
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Pending Errata and Addenda
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![$ \mathbb{Q}[G]$](http://images.planetmath.org:8080/cache/objects/5642/l2h/img4.png "$ \mathbb{Q}[G]$"){kind=small}
![$ \theta\in\mathbb{Q}[G]$](http://images.planetmath.org:8080/cache/objects/5642/l2h/img5.png "$ \theta\in\mathbb{Q}[G]$"){kind=small}
![$ \beta\in\mathbb{Z}[G]$](http://images.planetmath.org:8080/cache/objects/5642/l2h/img7.png "$ \beta\in\mathbb{Z}[G]$"){kind=small}
![$ \beta\theta\in\mathbb{Z}[G]$](http://images.planetmath.org:8080/cache/objects/5642/l2h/img8.png "$ \beta\theta\in\mathbb{Z}[G]$"){kind=small}
