Theorems · Theorem · commutative algebra
Ideal.exists_of_comap_eq_ker_sup
∀ {A : Type u_1} {B : Type u_2} [inst : Ring A] [inst_1 : Ring B] (f : A →+* B),
Function.Surjective ⇑f →
∀ {I : Ideal B} {J : Ideal A}, Ideal.comap f I = RingHom.ker f ⊔ J → ∀ {x : B}, x ∈ I → ∃ y ∈ J, f y = x- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- map_addproof · cited by 964
- Ideal.comapstatement and proof · cited by 443
- RingHom.kerstatement and proof · cited by 363
- Submodule.mem_supproof · cited by 73
- Ideal.mem_comapproof · cited by 54
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.eq_map_of_comap_eq_ker_supproof · cited by 2
- Ideal.mapCotangent_surjective_of_comap_eqproof · cited by 1
- Algebra.Extension.Cotangent.map_surjective_of_comap_eqproof · cited by 0