Theorems · Theorem · ring theory
NonUnitalRingHom.srange_eq_top_of_surjective
∀ {R : Type u} {S : Type v} [inst : NonUnitalNonAssocSemiring R] {F : Type u_1} [inst_1 : FunLike F R S]
[inst_2 : NonUnitalNonAssocSemiring S] [inst_3 : NonUnitalRingHomClass F R S] (f : F),
Function.Surjective ⇑f → NonUnitalRingHom.srange f = ⊤The range of a surjective non-unital ring homomorphism is the whole of the codomain.
- Cited by
- 2 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.
Cites8
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
- Top.topstatement · cited by 9,680
- FunLikestatement and proof · cited by 2,560
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- NonUnitalSubsemiringstatement · cited by 201
- NonUnitalRingHomClassstatement and proof · cited by 82
- NonUnitalRingHom.srangestatement · cited by 17
- NonUnitalRingHom.srange_eq_top_iff_surjectiveproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- NonUnitalSubsemiring.range_fstproof · cited by 1
- NonUnitalSubsemiring.range_sndproof · cited by 1