Theorems · Theorem · commutative algebra
AdicCompletion.ofTensorProduct_surjective_of_finite
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (M : Type u_2) [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[Module.Finite R M], Function.Surjective ⇑(AdicCompletion.ofTensorProduct I M)If M is a finite R-module, then the canonical map
AdicCompletion I R ⊗[R] M →ₗ AdicCompletion I M is surjective.
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- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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