Theorems · Theorem · commutative algebra
Ideal.comap_mono
∀ {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}
{K L : Ideal S} [inst_3 : RingHomClass F R S], K ≤ L → Ideal.comap f K ≤ Ideal.comap f L- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- Ideal.comapstatement and proof · cited by 443
- AddSubmonoid.toAddSubsemigroupproof · cited by 198
- AddSubsemigroup.carrierproof · cited by 198
- RingHomClassstatement and proof · cited by 193
- Submodule.toAddSubmonoidproof · cited by 162
- Set.preimage_monoproof · cited by 95
Cited by25
Results whose statement or proof uses this declaration.
- Ideal.comap_map_of_surjectiveproof · cited by 30
- Ideal.comap_isMaximal_of_surjectiveproof · cited by 8
- PrimeSpectrum.isClosed_image_of_stableUnderSpecializationproof · cited by 6
- ringKrullDim_le_of_surjectiveproof · cited by 4
- Ideal.exists_comap_eq_of_mem_minimalPrimesproof · cited by 4
- IsLocalization.minimalPrimes_mapproof · cited by 4
- Ideal.minimalPrimes_comap_of_surjectiveproof · cited by 3
- Ideal.comap_jacobson_of_surjectiveproof · cited by 2
- Ideal.comap_le_iff_le_mapproof · cited by 2
- Ideal.exists_minimalPrimes_comap_eqproof · cited by 2
- Ideal.ramificationIdx'_le_ramificationIdx'proof · cited by 2
- Ideal.IsMaximal.of_isLocalization_of_disjointproof · cited by 2