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

$FK=F(K)=K(F)$

$F(S)$ is the set of all $F$-rational expressions in finitely many elements of $S$.

References

• Roman, Steven (1995). Field Theory. New York: Springer-Verlag. ISBN 0-387-94407-9., especially chapter 2