Theorems · Theorem · ring theory

DirectSum.completeOrthogonalIdempotents_idempotent

∀ {R : Type u_1} {I : Type u_2} [inst : Semiring R] [inst_1 : DecidableEq I] (V : I → Ideal R)
  [inst_2 : DirectSum.Decomposition V] [inst_3 : Fintype I], CompleteOrthogonalIdempotents (DirectSum.idempotent V)

If a semiring can be decomposed into direct sum of finite left ideals Vᵢ where 1 = e₁ + ... + eₙ and eᵢ ∈ Vᵢ, then eᵢ is a family of complete orthogonal idempotents.

Defined in

Mathlib.Algebra.DirectSum.Idempotents

Cited by

0 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringDecidableEqDirectSum.DecompositionFintype