Theorems · Theorem · field theory
IntermediateField.restrictScalars_injective
∀ (K : Type u_1) {L : Type u_2} {L' : Type u_3} [inst : Field K] [inst_1 : Field L] [inst_2 : Field L']
[inst_3 : Algebra K L] [inst_4 : Algebra K L'] [inst_5 : Algebra L' L] [inst_6 : IsScalarTower K L' L],
Function.Injective (IntermediateField.restrictScalars K)- Cited by
- 8 results in Mathlib
- Foundations
- Depth 61 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 and proof · cited by 988
- IntermediateField.restrictScalarsstatement and proof · cited by 66
- IntermediateField.extproof · cited by 17
- IntermediateField.mem_restrictScalarsproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_eq_top_of_adjoin_eq_topproof · cited by 1
- Polynomial.irreducible_compproof · cited by 1
- IntermediateField.extendScalars_selfproof · cited by 0
- IntermediateField.extendScalars_topproof · cited by 0
- IntermediateField.restrictScalars_injproof · cited by 0
- IntermediateField.extendScalars_adjoinproof · cited by 0