Theorems · Theorem · field theory
IntermediateField.restrictScalars_adjoin
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (K : IntermediateField F E)
(S : Set E),
IntermediateField.restrictScalars F (IntermediateField.adjoin (↥K) S) = IntermediateField.adjoin F (↑K ∪ S)- Cited by
- 9 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- SetLike.coestatement and proof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- IntermediateField.restrictScalarsstatement and proof · cited by 66
- IntermediateField.adjoin_selfproof · cited by 6
- IntermediateField.adjoin_adjoin_leftproof · cited by 6
Cited by9
Results whose statement or proof uses this declaration.
- IntermediateField.sup_toSubalgebra_of_isAlgebraic_rightproof · cited by 6
- IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraicproof · cited by 5
- IntermediateField.Lifts.union_isExtendibleproof · cited by 1
- IntermediateField.restrictScalars_adjoin_eq_supproof · cited by 1
- Polynomial.irreducible_compproof · cited by 1
- IsGalois.sup_rightproof · cited by 0
- RatFunc.IntermediateField.adjoin_Xproof · cited by 0
- IntermediateField.extendScalars_adjoinproof · cited by 0