Theorems · Theorem · commutative algebra
Ideal.map_comap_of_surjective
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
[inst_3 : RingHomClass F R S], Function.Surjective ⇑f → ∀ (I : Ideal S), Ideal.map f (Ideal.comap f I) = I- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- Ideal.mapstatement and proof · cited by 692
- Ideal.comapstatement and proof · cited by 443
- RingHomClassstatement and proof · cited by 193
- Ideal.mem_map_of_memproof · cited by 71
- Ideal.map_le_iff_le_comapproof · cited by 60
Cited by14
Results whose statement or proof uses this declaration.
- Algebra.FinitePresentation.ker_fG_of_surjectiveproof · cited by 7
- Ideal.giMapComapproof · cited by 6
- Ideal.map_jacobson_of_surjectiveproof · cited by 4
- isJacobsonRing_of_surjectiveproof · cited by 4
- Ideal.le_map_of_comap_le_of_surjectiveproof · cited by 4
- Ideal.map_comap_eq_self_of_equivproof · cited by 2
- Ideal.IsPrincipal.of_comapproof · cited by 1
- IsDedekindDomain.idealFactorsFunOfQuotHom_compproof · cited by 1
- Ideal.coheight_comap_of_surjectiveproof · cited by 1
- Ideal.map_radical_of_surjectiveproof · cited by 1
- IsLocalRing.map_maximalIdeal_of_surjectiveproof · cited by 1
- Ideal.comap_le_comap_iff_of_surjectiveproof · cited by 0