The Stacks project

Definition 9.27.1. Consider a diagram

9.27.1.1
\begin{equation} \label{fields-equation-inside-omega} \vcenter { \xymatrix{ L \ar[r] & \Omega \\ k \ar[r] \ar[u] & K \ar[u] } } \end{equation}

of field extensions. The compositum of $K$ and $L$ in $\Omega $ written $KL$ is the smallest subfield of $\Omega $ containing both $L$ and $K$.

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View Definition 9.27.1 as pdf