Theorems · Theorem · ring theory
NonUnitalRingHom.range_eq_top
∀ {R : Type u} {S : Type v} [inst : NonUnitalNonAssocRing R] [inst_1 : NonUnitalNonAssocRing S] {f : R →ₙ+* S},
f.range = ⊤ ↔ Function.Surjective ⇑f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- NonUnitalNonAssocRingstatement and proof · cited by 354
- NonUnitalSubringstatement · cited by 185
- NonUnitalRingHomstatement and proof · cited by 157
- SetLike.ext'_iffproof · cited by 78
- Set.range_eq_univproof · cited by 50
- NonUnitalRingHom.rangestatement · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- NonUnitalRingHom.range_eq_top_of_surjectiveproof · cited by 0