Theorems · Theorem · ring theory

CompleteOrthogonalIdempotents.bijective_pi

∀ {R : Type u_1} [inst : CommRing R] {I : Type u_3} [inst_1 : Fintype I] {e : I → R},
  CompleteOrthogonalIdempotents e → Function.Bijective ⇑(RingHom.pi fun i => Ideal.Quotient.mk (Ideal.span {1 - e i}))

A family of complete orthogonal idempotents induces an isomorphism R ≃+* ∏ R ⧸ ⟨1 - eᵢ⟩

Defined in

Mathlib.RingTheory.Idempotents

Cited by

2 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFintype