Let $K/F$ be a cyclic field extension of degree $n$, let $\sigma$ be a generator of $Gal(K/F)$ and $u\in F^\times$. Denote $(K/F,'\sigma, u)=\oplus_{i=0}^{n-1}Kz^i$ where $z$ is a symbol, and define a multiplication by $zx=\sigma(x)z$ and $z^n=u$. This is a central simple $F$ algebra of degree $n$.
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