Theorems · Theorem · commutative algebra
Ideal.Fiber.lift_residueField_surjective
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[Algebra.FiniteType R S] (p : Ideal R) [inst_4 : p.IsPrime] (q : Ideal S) [inst_5 : q.IsPrime] [inst_6 : q.LiesOver p]
[Algebra.QuasiFiniteAt R q] [inst_8 : Algebra (Localization.AtPrime p) (Localization.AtPrime q)]
[inst_9 : Localization.AtPrime.IsLiesOverAlgebra p q],
Function.Surjective
⇑(Algebra.TensorProduct.lift (Algebra.ofId p.ResidueField q.ResidueField)
(IsScalarTower.toAlgHom R S q.ResidueField) ⋯)- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites56
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
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- AlgHomstatement · cited by 3,236
- one_mulproof · cited by 2,841
- TensorProductstatement and proof · cited by 2,545
- TensorProduct.tmulproof · cited by 1,182
- RingHom.compproof · cited by 899
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_topproof · cited by 1