Composite field (mathematics)

A composite field or compositum of fields is an object of study in field theory. Let K be a field, and let ${\displaystyle E_{1}}$, ${\displaystyle E_{2}}$ be subfields of K. Then the (internal) composite^[1] of ${\displaystyle E_{1}}$ and ${\displaystyle E_{2}}$ is the field defined as the intersection of all subfields of K containing both ${\displaystyle E_{1}}$ and ${\displaystyle E_{2}}$. The composite is commonly denoted ${\displaystyle E_{1}E_{2}}$.