gcommRing — Mathlib

English

There exists a complete set of orthogonal idempotents corresponding to a direct-sum decomposition.

Русский

Существует полное ортогональное разложение на идемпотенты.

LaTeX

$$CompleteOrthogonalIdempotents (DirectSum.idempotent V)$$

Lean4

/-- Build a `DirectSum.GCommRing` instance for a collection of additive submonoids. -/
instance gcommRing [AddCommMonoid ι] [CommRing R] [SetLike σ R] [AddSubgroupClass σ R] (A : ι → σ)
    [SetLike.GradedMonoid A] : DirectSum.GCommRing fun i => A i :=
  { SetLike.gCommMonoid A, SetLike.gring A with }

Похожие утверждения