Theorems · Theorem · field theory
IntermediateField.adjoin_map
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (S : Set E) {E' : Type u_3}
[inst_3 : Field E'] [inst_4 : Algebra F E'] (f : E →ₐ[F] E'),
IntermediateField.map f (IntermediateField.adjoin F S) = IntermediateField.adjoin F (⇑f '' S)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.imagestatement and proof · cited by 5,609
- AlgHomstatement and proof · cited by 3,236
- le_antisymmproof · cited by 2,068
- IntermediateFieldstatement · cited by 988
- RingHomClass.toRingHomproof · cited by 746
- IntermediateField.adjoinstatement and proof · cited by 382
- IntermediateField.toSubalgebraproof · cited by 134
Cited by5
Results whose statement or proof uses this declaration.
- IntermediateField.lift_adjoinproof · cited by 5
- Algebra.FormallyEtale.of_isSeparableproof · cited by 3
- FiniteGaloisIntermediateField.adjoin_mapproof · cited by 1
- IntermediateField.essFiniteType_iffproof · cited by 1
- IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosedproof · cited by 1