DirectSum.idempotent

{R : Type u_1} →
  {I : Type u_2} →
    [inst : Semiring R] → [inst_1 : DecidableEq I] → (V : I → Ideal R) → [DirectSum.Decomposition V] → I → R

The decomposition of (1 : R) where 1 = e₁ + e₂ + ⋯ + eₙ which is induced by the decomposition of the semiring R = V1 ⊕ V2 ⊕ ⋯ ⊕ Vn.

Defined in: Mathlib.Algebra.DirectSum.Idempotents
Cited by: 3 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring DecidableEq DirectSum.Decomposition

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