Composite field (mathematics)

A composite field 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.