Theorems · Theorem · commutative algebra

AdicCompletion.ofTensorProductEquivOfFiniteNoetherian.congr_simp

∀ {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],
  AdicCompletion.ofTensorProductEquivOfFiniteNoetherian I M = AdicCompletion.ofTensorProductEquivOfFiniteNoetherian I M

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

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites11

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

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
Idealstatement and proof · cited by 4,748
LinearEquivstatement · cited by 3,317
TensorProductstatement · cited by 2,545
Module.Finitestatement and proof · cited by 1,032
IsNoetherianRingstatement and proof · cited by 268
AdicCompletionstatement · cited by 160
AdicCompletion.ofTensorProductEquivOfFiniteNoetherianstatement and proof · cited by 6

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.