Definition 59.61.4. Let $K$ be a field. The *Brauer group* of $K$ is the set $\text{Br} (K)$ of similarity classes of finite central simple algebras over $K$, endowed with the group law induced by tensor product (over $K$). The class of $A$ in $\text{Br}(K)$ is denoted by $[A]$. The neutral element is $[K] = [\text{Mat}(d \times d, K)]$ for any $d \geq 1$.

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