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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
Assumes
SemiringSemiringFunLikeRingHomClass

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ideal.comap_map_of_surjective · cited by 30Ideal.comap_map_of_surjec…Ideal.comap_isMaximal_of_surjective · cited by 8Ideal.comap_isMaximal_of_…PrimeSpectrum.isClosed_image_of_stableUnderSpecialization · cited by 6PrimeSpectrum.isClosed_im…ringKrullDim_le_of_surjective · cited by 4ringKrullDim_le_of_surjec…Ideal.exists_comap_eq_of_mem_minimalPrimes · cited by 4Ideal.exists_comap_eq_of_…IsLocalization.minimalPrimes_map · cited by 4IsLocalization.minimalPri…Ideal.minimalPrimes_comap_of_surjective · cited by 3Ideal.minimalPrimes_comap…Ideal.comap_jacobson_of_surjective · cited by 2Ideal.comap_jacobson_of_s…Ideal.comap_le_iff_le_map · cited by 2Ideal.comap_le_iff_le_mapIdeal.exists_minimalPrimes_comap_eq · cited by 2Ideal.exists_minimalPrime…Ideal.ramificationIdx'_le_ramificationIdx' · cited by 2Ideal.ramificationIdx'_le…Ideal.IsMaximal.of_isLocalization_of_disjoint · cited by 2IsMaximal.of_isLocalizati…Ideal.map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimes · cited by 1Ideal.map_sup_mem_minimal…Ideal.map_under_le_under_map · cited by 1Ideal.map_under_le_under_…Ideal.comap_lt_comap_of_root_mem_sdiff · cited by 1Ideal.comap_lt_comap_of_r…DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringIdeal · cited by 4748IdealFunLike · cited by 2560FunLikeIdeal.comap · cited by 443Ideal.comapAddSubmonoid.toAddSubsemigroup · cited by 198AddSubmonoid.toAddSubsemi…AddSubsemigroup.carrier · cited by 198AddSubsemigroup.carrierRingHomClass · cited by 193RingHomClassSubmodule.toAddSubmonoid · cited by 162Submodule.toAddSubmonoidSet.preimage_mono · cited by 95Set.preimage_monoIdeal.comap_monoCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by25

Results whose statement or proof uses this declaration.