 Linearly disjoint field extensions

ID: linearly-disjoint-field-extensions

Codex  0 Created 2026-09-24 Updated 2026-09-24

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_{1} L_{2} : K] = [L_{1} : K] [L_{2} : K] .

Extensions of coprime finite degrees are linearly disjoint.

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