Theorems · Theorem · commutative algebra
Ideal.eq_of_comap_eq_comap_of_bijective_residueFieldMap
∀ {R : Type u_1} {R' : Type u_2} {S : Type u_3} [inst : CommRing R] [inst_1 : CommRing R'] [inst_2 : CommRing S]
[inst_3 : Algebra R R'] [inst_4 : Algebra R S] {p : Ideal R} {q : Ideal R'} [inst_5 : p.IsPrime] [inst_6 : q.IsPrime]
[inst_7 : q.LiesOver p],
Function.Bijective ⇑(Ideal.ResidueField.mapₐ p q (Algebra.ofId R R') ⋯) →
∀ (P₁ P₂ : Ideal (TensorProduct R R' S)) [P₁.IsPrime] [P₂.IsPrime] [P₁.LiesOver q] [P₂.LiesOver q],
Ideal.comap Algebra.TensorProduct.includeRight.toRingHom P₁ =
Ideal.comap Algebra.TensorProduct.includeRight.toRingHom P₂ →
P₁ = P₂- Defined in
- Mathlib.RingTheory.Etale.QuasiFinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- AlgHomstatement · cited by 3,236
- TensorProductstatement and proof · cited by 2,545
- Function.Bijectivestatement and proof · cited by 863
- Ideal.IsPrimestatement and proof · cited by 827
- AlgHom.toRingHomstatement and proof · cited by 490
- Ideal.primeComplstatement · cited by 462
- Ideal.comapstatement and proof · cited by 443
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_auxproof · cited by 1