Theorems · Definition · commutative algebra

Ideal.quotientInfToPiQuotient

{R : Type u} →
  [inst : Ring R] →
    {ι : Type u_1} → (I : ι → Ideal R) → [inst_1 : ∀ (i : ι), (I i).IsTwoSided] → R ⧸ ⨅ i, I i →+* (i : ι) → R ⧸ I i

The homomorphism from R/(⋂ i, f i) to ∏ i, (R / f i) featured in the Chinese Remainder Theorem. It is bijective if the ideals f i are coprime.

Defined in

Mathlib.RingTheory.Ideal.Quotient.Operations

Cited by

6 results in Mathlib

Foundations

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

Assumes

RingIdeal.IsTwoSided