I know that $A$ is an central simple álgebra over a field $F$, then $[A]$ has finite order in the Brauer group. But, how to prove it?
I appreciate any hint
2026-04-03 15:47:48.1775231268
Finite order of an element in Brauer group.
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It corresponds to a cohomology class in $H^2(G,K^*)$ for some finite Galois extension $K/F$ with Galois group $G$. Cohomology groups with respect to a finite group $G$ are (except for $H^0$) annihilated by $|G|$.