Theorems · Theorem · field theory
separableClosure.eq_restrictScalars_of_isSeparable
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type w) [inst_3 : Field K] [inst_4 : Algebra F K] [inst_5 : Algebra E K] [inst_6 : IsScalarTower F E K] [Algebra.IsSeparable F E], separableClosure F K = IntermediateField.restrictScalars F (separableClosure E K)
If K / E / F is a field extension tower, such that E / F is separable, then
separableClosure F K is equal to separableClosure E K.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerstatement and proof · cited by 3,896
- IntermediateFieldstatement · cited by 988
- LE.le.antisymmproof · cited by 507
- Algebra.IsSeparablestatement and proof · cited by 210
- IntermediateField.restrictScalarsstatement and proof · cited by 66
- separableClosurestatement and proof · cited by 55
- separableClosure.le_restrictScalarsproof · cited by 4
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Field.lift_rank_mul_lift_sepDegree_of_isSeparableproof · cited by 2
- Field.insepDegree_eq_of_isSeparableproof · cited by 1