Theorems · Theorem · commutative algebra

AdicCompletion.tensor_map_id_left_injective_of_injective

∀ {R : Type u} [inst : CommRing R] (I : Ideal R) [IsNoetherianRing R] {M : Type u} [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] {N : Type u} [inst_4 : AddCommGroup N] [inst_5 : Module R N] {f : M →ₗ[R] N} [Module.Finite R M]
  [Module.Finite R N],
  Function.Injective ⇑f → Function.Injective ⇑(TensorProduct.AlgebraTensorModule.map LinearMap.id f)

Defined in: Mathlib.RingTheory.AdicCompletion.AsTensorProduct
Cited by: 0 results in Mathlib
Foundations: Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsNoetherianRing AddCommGroup Module AddCommGroup Module Module.Finite Module.Finite

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DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement and proof · cited by 10,215
Idealstatement and proof · cited by 4,748
TensorProductstatement and proof · cited by 2,545
LinearEquiv.symmproof · cited by 1,461
Module.Finitestatement and proof · cited by 1,032
LinearMap.idstatement · cited by 625
IsNoetherianRingstatement and proof · cited by 268

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