Order of a finite division ring
Order of a finite division ring
Prove that the order of a finite division ring is power of a prime.
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Re: Order of a finite division ring
Let \( \displaystyle D \) be a finite division ring. Then, by Wedderburn's Little Theorem, \( \displaystyle D \) is a finite field. It is a well-known result (from Galois Theory - we regard \( \displaystyle D \) as a vector space over its prime field, which has to be (isomorphic to) \( \displaystyle \mathbb{Z}_{p} \) ) that every such field contains \( \displaystyle p^{n} \) elements for some prime number \( \displaystyle p \) and some natural number \( \displaystyle n \).
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