linearDisjoint_iff — Mathlib

English

For A ⊆ E, L is a field with E over F, A is linearly disjoint from L iff A as a subalgebra is linearly disjoint from the range of IsScalarTower toAlgHom F L E.

Русский

Для A ⊆ E, L — поле, линейно раздельны от L тогда и только тогда, когда A как подалгебра линейно неразделима от образа IsScalarTower toAlgHom F L E.

LaTeX

$$$A\\,\\text{LinearDisjoint } L \\iff A^{\\text{toSubalgebra}} \\text{LinearDisjoint } (\\mathrm{IsScalarTower.toAlgHom} F L E)\\text{.range}$$$

Lean4

theorem linearDisjoint_iff : A.LinearDisjoint L ↔ A.toSubalgebra.LinearDisjoint (IsScalarTower.toAlgHom F L E).range :=
  Iff.rfl

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