Field compositum
= Field compositum
= Compositum
{synonym}
Inside a common overfield, the compositum $L_1L_2$ is the smallest field containing both $L_1$ and $L_2$.
The multiplication image of the <tensor product of fields> in a common overfield generates the compositum as a field. For algebraic extensions that image is already a field; in general it need not be. The compositum is therefore distinct from the tensor product algebra.