Theorems · Definition · field theory
RingHom.eqLocusField
{K : Type u} → [inst : DivisionRing K] → {L : Type v} → [inst_1 : Semiring L] → (K →+* L) → (K →+* L) → Subfield KThe subfield of elements x : R such that f x = g x, i.e.,
the equalizer of f and g as a subfield of R
- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingSemiring
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Set.ofPredproof · cited by 6,101
- DivisionRingstatement and proof · cited by 1,062
- Subringproof · cited by 602
- Subfieldstatement · cited by 303
- RingHom.eqLocusproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- RingHom.eqOn_field_closureproof · cited by 1
- RingHom.mem_eqLocusFieldstatement · cited by 0