Theorems · Theorem · commutative algebra

Module.FaithfullyFlat.lTensor_injective_iff_injective

∀ (R : Type u) (M : Type v) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_4}
  {N' : Type u_5} [inst_3 : AddCommGroup N] [inst_4 : AddCommGroup N'] [inst_5 : Module R N] [inst_6 : Module R N']
  (f : N →ₗ[R] N') [Module.FaithfullyFlat R M], Function.Injective ⇑(LinearMap.lTensor M f) ↔ Function.Injective ⇑f

Defined in

Mathlib.RingTheory.Flat.FaithfullyFlat.Basic

Cited by

4 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupAddCommGroupModuleModuleModule.FaithfullyFlat