Theorems · Theorem · commutative algebra

AdicCompletion.sumInv_comp_sum

∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {ι : Type u_6} (M : ι → Type u_7)
  [inst_1 : (i : ι) → AddCommGroup (M i)] [inst_2 : (i : ι) → Module R (M i)] [inst_3 : Fintype ι]
  [inst_4 : DecidableEq ι], AdicCompletion.sumInv I M ∘ₗ AdicCompletion.sum I M = LinearMap.id

Defined in: Mathlib.RingTheory.AdicCompletion.Functoriality
Cited by: 0 results in Mathlib
Foundations: Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module Fintype DecidableEq

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
Top.topproof · cited by 9,680
Fintypestatement and proof · cited by 7,736
Idealstatement and proof · cited by 4,748
LinearMap.compstatement · cited by 1,642
LinearMap.idstatement · cited by 625
DirectSumstatement and proof · cited by 446

Cited by1

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AdicCompletion.sumEquivOfFintypeproof · cited by 3