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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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I have just merged the two accounts. –  Mariano Suárez-Alvarez Mar 7 '12 at 1:47
    
For reader reference: math.stackexchange.com/q/117318/22405 –  Brett Frankel Mar 7 '12 at 1:48
    
Thank you for merging! –  user Mar 7 '12 at 1:48
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