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Inside a common overfield, the compositum $L_1{L}_2$ 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.

More generally, two field extensions inside a common overfield are linearly disjoint field extensions when the multiplication map from their tensor product of fields into that overfield is injective. The following basis criterion is the finite-degree case.

Finite extensions $L_1/K$ and $L_2/K$ are linearly disjoint when products of basis elements form a basis of their compositum. In particular,Extensions of coprime finite degrees are linearly disjoint.

The tensor product of fields $L{\otimes }_{K}M$ is a $K$-algebra, not necessarily a field. If $L$ and $M$ sit in one overfield, the map $l\otimes m\mapsto lm$ has an image that generates their compositum as a field. When the extensions are algebraic, this image is already a field. Injectivity of this multiplication map is equivalent to linear disjointness.