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...)