= Linear disjointness
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= Linearly disjoint field extensions
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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,
$$
[L_1L_2:K]=[L_1:K][L_2:K].
$$
Extensions of coprime finite degrees are linearly disjoint.
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