= Brauer class
{c}
{title2=$[A]\in\operatorname{Br}(K)$}
The Brauer class of a <central simple algebra> is its equivalence class under adjoining matrix-algebra factors. Two algebras have the same class exactly when their central division-algebra representatives are isomorphic. The zero class consists of split matrix algebras; the inverse of $[A]$ is the class of the <opposite algebra>. For a <cyclic algebra> $(L/K,\sigma,a)$, the class is zero exactly when $a$ is a <field norm> from $L$.
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