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Theorems · Theorem · field theory

IntermediateField.linearDisjoint_iff

∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (A : IntermediateField F E)
  (L : Type w) [inst_3 : Field L] [inst_4 : Algebra F L] [inst_5 : Algebra L E] [inst_6 : IsScalarTower F L E],
  A.LinearDisjoint L ↔ A.LinearDisjoint (IsScalarTower.toAlgHom F L E).range
Defined in
Mathlib.FieldTheory.LinearDisjoint
Cited by
3 results in Mathlib
Foundations
Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebraFieldAlgebraAlgebraIsScalarTower
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IntermediateField.linearDisjoint_iff' · cited by 19IntermediateField.linearD…IntermediateField.LinearDisjoint.map'' · cited by 0LinearDisjoint.map''IntermediateField.LinearDisjoint.map' · cited by 0LinearDisjoint.map'Algebra · cited by 11388AlgebraField · cited by 7404FieldIsScalarTower · cited by 3896IsScalarTowerIntermediateField · cited by 988IntermediateFieldIsScalarTower.toAlgHom · cited by 232IsScalarTower.toAlgHomAlgHom.range · cited by 169AlgHom.rangeIntermediateField.toSubalgebra · cited by 134IntermediateField.toSubal…IntermediateField.LinearDisjoint · cited by 82IntermediateField.LinearD…Subalgebra.LinearDisjoint · cited by 75Subalgebra.LinearDisjointIntermediateField.linearDisjo…CITED BYCITES

Cites9

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Cited by3

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