Definition 11.8.1. Let $A$ be a finite central simple $k$-algebra. We say a field extension $k'/k$ splits $A$, or $k'$ is a splitting field for $A$ if $A \otimes _ k k'$ is a matrix algebra over $k'$.
Definition 11.8.1. Let $A$ be a finite central simple $k$-algebra. We say a field extension $k'/k$ splits $A$, or $k'$ is a splitting field for $A$ if $A \otimes _ k k'$ is a matrix algebra over $k'$.
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