Theorems · Theorem · commutative algebra

Module.FaithfullyFlat.rTensor_reflects_triviality

∀ (R : Type u) (M : Type v) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [Module.FaithfullyFlat R M] (N : Type u_1) [inst_4 : AddCommGroup N] [inst_5 : Module R N]
  [h : Subsingleton (TensorProduct R N M)], Subsingleton N

Defined in: Mathlib.RingTheory.Flat.FaithfullyFlat.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module Module.FaithfullyFlat AddCommGroup Module Subsingleton

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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
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
TensorProductstatement and proof · cited by 2,545
Nontrivialproof · cited by 2,416
Module.FaithfullyFlatstatement and proof · cited by 72

Cited by4

Results whose statement or proof uses this declaration.

Module.FaithfullyFlat.lTensor_reflects_trivialityproof · cited by 3
Module.FaithfullyFlat.rTensor_reflects_exactproof · cited by 2
Module.FaithfullyFlat.subsingleton_tensorProduct_iff_leftproof · cited by 1
Module.FaithfullyFlat.range_le_ker_of_exact_rTensorproof · cited by 1