Theorems · Definition · field theory
Subfield.map
{K : Type u} → {L : Type v} → [inst : DivisionRing K] → [inst_1 : DivisionRing L] → (K →+* L) → Subfield K → Subfield LThe image of a subfield along a ring homomorphism is a subfield.
- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 53 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.
Cites6
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
- Subringproof · cited by 602
- Subfieldstatement and proof · cited by 303
- Subring.mapproof · cited by 33
- Subfield.toSubringproof · cited by 23
Cited by31
Results whose statement or proof uses this declaration.
- RingHom.fieldRangeproof · cited by 40
- Subfield.gc_map_comapstatement · cited by 7
- RingHom.fieldRange_eq_mapstatement · cited by 6
- Subfield.lift_relrank_comapstatement and proof · cited by 4
- Subfield.lift_relrank_comap_comap_eq_lift_relrank_infproof · cited by 4
- Subfield.lift_relrank_map_mapstatement · cited by 4
- Subfield.map_botstatement · cited by 3
- Subfield.map_comap_eqstatement and proof · cited by 3
- IsFractionRing.ringHom_fieldRange_eq_of_comp_eqproof · cited by 3
- ZMod.fieldRange_castHom_eq_botproof · cited by 2
- Subfield.map_infstatement and proof · cited by 2
- Subfield.map_le_iff_le_comapstatement · cited by 1