Theorems · Theorem · commutative algebra
Ideal.surjectiveOnStalks_residueField
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) [inst_1 : I.IsPrime],
(algebraMap R I.ResidueField).SurjectiveOnStalks- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIdeal.IsPrime
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplstatement and proof · cited by 462
- Localization.AtPrimestatement and proof · cited by 299
- IsLocalRing.ResidueFieldstatement · cited by 156
- Ideal.Quotient.mk_surjectiveproof · cited by 134
- Ideal.ResidueFieldstatement · cited by 119
- RingHom.SurjectiveOnStalksstatement · cited by 26
- RingHom.surjectiveOnStalks_of_surjectiveproof · cited by 7
- RingHom.SurjectiveOnStalks.compproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.ResidueField.exists_smul_eq_tmul_oneproof · cited by 1
- Ideal.Fiber.lift_residueField_surjectiveproof · cited by 1
- Algebra.IsUnramifiedAt.residueFieldproof · cited by 0