Composite field (mathematics)

A composite field or compositum of fields is an object of study in field theory. Let L be a field, and let F, K be subfields of L. Then the (internal) composite of F and K is defined to be the intersection of all subfields of L containing both F and K. The composite is commonly denoted FK. When F and K are not regarded as subfields of a common field then the (external) composite is defined using the tensor product of fields.

It also can be defined using field of fractions

${\displaystyle FK=F(K)=K(F)}$

${\displaystyle F(S)}$ is the set of all ${\displaystyle F}$-rational expressions in finitely many elements of ${\displaystyle S}$.[1]