Theorems · Theorem · commutative algebra
IsLocalHom.of_surjective
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [Nontrivial S] [IsLocalRing R] (f : R →+* S),
Function.Surjective ⇑f → IsLocalHom f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Nontrivialstatement and proof · cited by 2,416
- Ideal.mapproof · cited by 692
- Eq.leproof · cited by 605
- Ideal.IsMaximalproof · cited by 452
- Ideal.comapproof · cited by 443
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealproof · cited by 297
Cited by4
Results whose statement or proof uses this declaration.
- IsLocalRing.exists_maximalIdeal_pow_le_of_isArtinianRing_quotientproof · cited by 2
- IsLocalRing.map_maximalIdeal_of_surjectiveproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_algHom_localizationproof · cited by 1
- Function.Surjective.isLocalHomproof · cited by 0