Linear disjointness

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.