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I asked this question: Brauer group of a finite field is trivial and then I accidentally logged out and I don't know how to log back on, so I had to create a new account.

So my question was: I know that finite skew fields are field, but how does it follow from this that the Brauer group of a finite field is trivial. As someone wrote, I see that it follows if the only division algebra with finite center is the finite center (field). So how do I see this fact? (being a bit slow here...)

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    http://en.wikipedia.org/wiki/Wedderburn%27s_little_theorem2012-03-07
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    I have just merged the two accounts.2012-03-07
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    For reader reference: http://math.stackexchange.com/q/117318/224052012-03-07

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