Theorems · Theorem · field theory
AlgHom.fieldRange_eq_map
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {K : Type u_3}
[inst_3 : Field K] [inst_4 : Algebra F K] (f : E →ₐ[F] K), f.fieldRange = IntermediateField.map f ⊤- Cited by
- 4 results in Mathlib
- Foundations
- Depth 85 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.
- Algebrastatement and proof · cited by 11,388
- Top.topstatement · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- AlgHomstatement and proof · cited by 3,236
- IntermediateFieldstatement · cited by 988
- Set.image_univproof · cited by 322
- IntermediateField.mapstatement · cited by 62
- SetLike.ext'proof · cited by 60
- AlgHom.fieldRangestatement · cited by 57
Cited by4
Results whose statement or proof uses this declaration.
- IntermediateField.lift_topproof · cited by 6
- Algebra.FormallyEtale.of_isSeparableproof · cited by 3
- AlgHom.fieldRange_of_normalproof · cited by 2
- IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosedproof · cited by 1