Theorems · Theorem · commutative algebra

AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply

∀ {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 : TensorProduct R (AdicCompletion I R) M),
  (AdicCompletion.ofTensorProductEquivOfFiniteNoetherian I M) x = (AdicCompletion.ofTensorProduct I M) x

Defined in: Mathlib.RingTheory.AdicCompletion.AsTensorProduct
Cited by: 0 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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DFunLike.coestatement · 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
Idealstatement and proof · cited by 4,748
LinearEquivstatement · cited by 3,317
TensorProductstatement and proof · cited by 2,545
Module.Finitestatement and proof · cited by 1,032
IsNoetherianRingstatement and proof · cited by 268
AdicCompletionstatement and proof · cited by 160

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