Theorems · Theorem · commutative algebra

Ideal.quotientMap_mk

∀ {R : Type u} [inst : Ring R] {S : Type v} [inst_1 : Ring S] {J : Ideal R} {I : Ideal S} [inst_2 : I.IsTwoSided]
  [inst_3 : J.IsTwoSided] {f : R →+* S} {H : J ≤ Ideal.comap f I} {x : R},
  (Ideal.quotientMap I f H) ((Ideal.Quotient.mk J) x) = (Ideal.Quotient.mk I) (f x)

Defined in

Mathlib.RingTheory.Ideal.Quotient.Operations

Cited by

9 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingRingIdeal.IsTwoSidedIdeal.IsTwoSided