Theorems · Theorem · field theory
separableClosure.le_restrictScalars
∀ (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], separableClosure F K ≤ IntermediateField.restrictScalars F (separableClosure E K)
If K / E / F is a field extension tower, then separableClosure F K is contained in
separableClosure E K.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IntermediateField.restrictScalarsstatement · cited by 66
- separableClosurestatement · cited by 55
- IsSeparable.tower_topproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- separableClosure.eq_restrictScalars_of_isSeparableproof · cited by 2
- Field.finInsepDegree_top_le_finInsepDegree_of_isScalarTowerproof · cited by 1
- Field.insepDegree_top_le_insepDegree_of_isScalarTowerproof · cited by 1
- separableClosure.adjoin_leproof · cited by 0