Theorems · Theorem · ring theory
NonUnitalRingHom.range_eq_top_of_surjective
∀ {R : Type u} {S : Type v} [inst : NonUnitalNonAssocRing R] [inst_1 : NonUnitalNonAssocRing S] (f : R →ₙ+* S),
Function.Surjective ⇑f → f.range = ⊤The range of a surjective ring homomorphism is the whole of the codomain.
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- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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
- NonUnitalNonAssocRingstatement and proof · cited by 354
- NonUnitalSubringstatement · cited by 185
- NonUnitalRingHomstatement and proof · cited by 157
- NonUnitalRingHom.rangestatement · cited by 12
- NonUnitalRingHom.range_eq_topproof · cited by 1
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