Theorems · Definition · field theory
RingHom.rangeRestrictField
{K : Type u} → {L : Type v} → [inst : DivisionRing K] → [inst_1 : DivisionRing L] → (f : K →+* L) → K →+* ↥f.fieldRangeRestriction of a ring homomorphism to its range interpreted as a subfield.
- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 55 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement · cited by 303
- RingHom.fieldRangestatement · cited by 40
- RingHom.rangeSRestrictproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- RingHom.rangeRestrictFieldEquivproof · cited by 2
- Subfield.card_botproof · cited by 2
- RingHom.coe_rangeRestrictFieldstatement · cited by 1
- RingHom.rangeRestrictField_bijectivestatement · cited by 1
- Complex.uniformContinuous_ringHom_eq_id_or_conjproof · cited by 1