Theorems · Theorem · field theory
algebraicClosure.le_restrictScalars
∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type u_3) [inst_3 : Field K] [inst_4 : Algebra F K] [inst_5 : Algebra E K] [inst_6 : IsScalarTower F E K], algebraicClosure F K ≤ IntermediateField.restrictScalars F (algebraicClosure E K)
If K / E / F is a field extension tower, then algebraicClosure F K is contained in
algebraicClosure E K.
- Defined in
- Mathlib.FieldTheory.AlgebraicClosure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- algebraicClosurestatement and proof · cited by 22
- mem_algebraicClosure_iffproof · cited by 5
- IsAlgebraic.tower_topproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- algebraicClosure.adjoin_leproof · cited by 0
- algebraicClosure.eq_restrictScalars_of_isAlgebraicproof · cited by 0