Brauer group
= Brauer group
{c}
{title2=$\operatorname{Br}(k)$}
{wiki}
The Brauer group of a field $k$ consists of <Morita equivalence> classes of central simple $k$-algebras. Multiplication is induced by tensor product, the identity is $[k]$, and the inverse of $[A]$ is the class of the opposite algebra $A^{\mathrm{op}}$.