Theorems · Definition · field theory
RingHom.fieldRange
{K : Type u} → {L : Type v} → [inst : DivisionRing K] → [inst_1 : DivisionRing L] → (K →+* L) → Subfield LThe range of a ring homomorphism, as a subfield of the target. See Note [range copy pattern].
- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingDivisionRing
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.
- DFunLike.coeproof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Top.topproof · cited by 9,680
- Set.rangeproof · cited by 4,705
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement · cited by 303
- Subfield.mapproof · cited by 30
- Subfield.copyproof · cited by 2
Cited by43
Results whose statement or proof uses this declaration.
- AlgHom.fieldRangeproof · cited by 57
- RingHom.fieldRange_eq_mapstatement · cited by 6
- NumberField.InfinitePlace.mk_eq_iffproof · cited by 5
- RingHom.rangeRestrictFieldstatement · cited by 4
- Subfield.lift_relrank_comap_comap_eq_lift_relrank_infstatement and proof · cited by 4
- Subfield.relrank_eq_one_iffproof · cited by 3
- Subfield.lift_rank_comapstatement · cited by 3
- Subfield.lift_relrank_comap_comap_eq_lift_relrank_of_lestatement and proof · cited by 3
- Subfield.map_comap_eqstatement and proof · cited by 3
- IsFractionRing.ringHom_fieldRange_eq_of_comp_eqstatement · cited by 3
- Complex.subfield_eq_of_closedstatement · cited by 2
- ZMod.fieldRange_castHom_eq_botstatement · cited by 2