Theorems · Theorem · field theory
RingHom.fieldRange_eq_top_iff
∀ {K : Type u} {L : Type v} [inst : DivisionRing K] [inst_1 : DivisionRing L] {f : K →+* L},
f.fieldRange = ⊤ ↔ Function.Surjective ⇑f- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 2 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Top.topstatement · cited by 9,680
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement · cited by 303
- SetLike.ext'_iffproof · cited by 78
- Set.range_eq_univproof · cited by 50
- RingHom.fieldRangestatement · cited by 40
Cited by2
Results whose statement or proof uses this declaration.