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# Wedderburn’s theorem

A finite division ring is a field.

One of the many consequences of this theorem is that for a finite projective plane, Desargues’ theorem implies Pappus’ theorem.

Related:

NonZeroDivisorsOfFiniteRing, JosephWedderburn

Synonym:

Wedderburn theorem

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

12E15*no label found*

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## Comments

## Wedderburn Theorem

It would be instructive to have a look on a new proof of Wedderburn Theorem (Any finite division ring is commutative), proof which I published in Amer. Math. Monthly (October 2003, by Nicolas Lichiardopol). W. Narkiewicz said me that is the most beautefull proof.

## Re: Wedderburn Theorem

I don' think many people have electronic access to 2003 monthly.

By the way, there's a book

"Proofs of the book"

(ref to Erdos idea)

where it's proved that theorem only using elementary concepts

(some basics about group actions, roots of unity, etc)

f

G -----> H G

p \ /_ ----- ~ f(G)

\ / f ker f

G/ker f