Theorems · Theorem · commutative algebra
RingHom.range_eq_top
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {f : R →+* S},
f.range = ⊤ ↔ Function.Surjective ⇑f- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
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
- RingHomstatement and proof · cited by 10,189
- 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
- Subringstatement · cited by 602
- NonAssocRingstatement and proof · cited by 483
- RingHom.rangestatement · cited by 138
- SetLike.ext'_iffproof · cited by 78
- Set.range_eq_univproof · cited by 50
Cited by4
Results whose statement or proof uses this declaration.
- RingHom.range_eq_top_of_surjectiveproof · cited by 1
- RingCon.range_mk'proof · cited by 0
- CommRingCat.HomTopology.isEmbedding_pushoutproof · cited by 0
- Submodule.traceDual_topproof · cited by 0