Theorems · Theorem · commutative algebra
RingHom.SurjectiveOnStalks.residueFieldMap_bijective
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S},
f.SurjectiveOnStalks →
∀ (I : Ideal R) [inst_2 : I.IsPrime] (J : Ideal S) [inst_3 : J.IsPrime] (hf : I = Ideal.comap f J),
Function.Bijective ⇑(Ideal.ResidueField.map I J f hf)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Function.Bijectivestatement · cited by 863
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplstatement · cited by 462
- Ideal.comapstatement and proof · cited by 443
- Localization.AtPrimestatement and proof · cited by 299
- IsLocalRing.maximalIdealproof · cited by 297
- RingHom.injectiveproof · cited by 187
- Ideal.Quotient.mk_surjectiveproof · cited by 134
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eqproof · cited by 1
- Ideal.Fiber.lift_residueField_surjectiveproof · cited by 1