Theorems · Definition · ring theory
NonUnitalRingHom.range
{R : Type u} →
{S : Type v} → [inst : NonUnitalNonAssocRing R] → [inst_1 : NonUnitalNonAssocRing S] → (R →ₙ+* S) → NonUnitalSubring SThe range of a ring homomorphism, as a NonUnitalSubring of the target.
See Note [range copy pattern].
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Top.topproof · cited by 9,680
- Set.rangeproof · cited by 4,705
- NonUnitalNonAssocRingstatement and proof · cited by 354
- NonUnitalSubringstatement · cited by 185
- NonUnitalRingHomstatement and proof · cited by 157
- NonUnitalSubring.mapproof · cited by 19
- NonUnitalSubring.copyproof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- NonUnitalRingHom.rangeRestrictstatement and proof · cited by 2
- RingEquiv.ofLeftInverse'statement and proof · cited by 2
- NonUnitalRingHom.mem_rangestatement · cited by 2
- NonUnitalRingHom.coe_rangestatement · cited by 2
- NonUnitalRingHom.range_eq_mapstatement · cited by 1
- NonUnitalRingHom.range_eq_topstatement · cited by 1
- NonUnitalRingHom.rangeRestrict_surjectivestatement and proof · cited by 0
- NonUnitalRingHom.range_eq_top_of_surjectivestatement · cited by 0
- RingEquiv.ofLeftInverse'_applystatement · cited by 0
- RingEquiv.ofLeftInverse'_symm_applystatement and proof · cited by 0
- NonUnitalRingHom.map_rangestatement and proof · cited by 0
- NonUnitalRingHom.mem_range_selfstatement · cited by 0