Theorems · Theorem · commutative algebra

AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of

∀ {R : Type u} [inst : CommRing R] (I : Ideal R) (M : Type u) [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : IsNoetherianRing R] [inst_4 : Module.Finite R M] (x : M),
  (AdicCompletion.ofTensorProductEquivOfFiniteNoetherian I M).symm ((AdicCompletion.of I M) x) = 1 ⊗ₜ[R] x

Defined in: Mathlib.RingTheory.AdicCompletion.AsTensorProduct
Cited by: 1 results in Mathlib
Foundations: Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsNoetherianRing Module.Finite

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AddCommGroupstatement and proof · cited by 12,871
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LinearEquiv.symmstatement and proof · cited by 1,461
one_smulproof · cited by 1,374
TensorProduct.tmulstatement and proof · cited by 1,182

Cited by1

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AdicCompletion.tensor_map_id_left_eq_mapproof · cited by 1