Theorems · Theorem · commutative algebra

Ideal.ker_quotientMap_mk

∀ {R : Type u} [inst : Ring R] {I J : Ideal R} [inst_1 : I.IsTwoSided] [inst_2 : J.IsTwoSided],
  RingHom.ker (Ideal.quotientMap (Ideal.map (Ideal.Quotient.mk I) J) (Ideal.Quotient.mk I) ⋯) =
    Ideal.map (Ideal.Quotient.mk J) I

Defined in: Mathlib.RingTheory.Ideal.Quotient.Operations
Cited by: 1 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring Ideal.IsTwoSided Ideal.IsTwoSided

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Cites21

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

RingHomstatement and proof · cited by 10,189
Ringstatement and proof · cited by 7,463
Idealstatement and proof · cited by 4,748
HasQuotient.Quotientstatement and proof · cited by 2,301
RingHom.compproof · cited by 899
Ideal.mapstatement and proof · cited by 692
Ideal.Quotient.mkstatement and proof · cited by 610
Ideal.comapproof · cited by 443
RingHom.kerstatement and proof · cited by 363
Ideal.IsTwoSidedstatement and proof · cited by 179
Ideal.Quotient.mk_surjectiveproof · cited by 134
Ideal.mk_kerproof · cited by 59

Cited by1

Results whose statement or proof uses this declaration.

Algebra.FormallySmooth.pi_iffproof · cited by 1