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Theorems · Theorem · commutative algebra

Ideal.comap_map_mk

∀ {R : Type u} [inst : Ring R] {I J : Ideal R} [inst_1 : I.IsTwoSided],
  I ≤ J → Ideal.comap (Ideal.Quotient.mk I) (Ideal.map (Ideal.Quotient.mk I) J) = J
Defined in
Mathlib.RingTheory.Ideal.Quotient.Operations
Cited by
2 results in Mathlib
Foundations
Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingIdeal.IsTwoSided
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Around this declaration

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

Ideal.finite_setOfPred_absNorm_eq · cited by 3Ideal.finite_setOfPred_ab…isDedekindDomainDvr.of_formallyUnramified · cited by 1isDedekindDomainDvr.of_fo…RingHom · cited by 10189RingHomRing · cited by 7463RingIdeal · cited by 4748IdealHasQuotient.Quotient · cited by 2301HasQuotient.QuotientIdeal.map · cited by 692Ideal.mapIdeal.Quotient.mk · cited by 610Quotient.mkIdeal.comap · cited by 443Ideal.comapIdeal.IsTwoSided · cited by 179Ideal.IsTwoSidedIdeal.comap_map_quotientMk · cited by 5Ideal.comap_map_quotientMkIdeal.comap_map_mkCITED BYCITES

Cites9

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Cited by2

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