Definition. composite field [2401]

Let $K_{1}, K_{2}$ be subfields of $K$. The composite field of $K_{1}$ and $K_{2}$, denoted $K_{1} K_{2}$, is the smallest subfield of $K$ containing both $K_{1}$ and $K_{2}$. Similarly, if $K_{1}, \dots, K_{n}$ are subfields of $K$, the composite field of $K_{1}, \dots, K_{n}$, denoted $K_{1}K_{2}\cdots K_{n}$ is the smallest subfield of $K$ containing both $K_{1}, \dots, K_{n}$.