Theorems · Theorem · commutative algebra

Module.FaithfullyFlat.subsingleton_tensorProduct_iff_right

∀ (R : Type u) (M : Type v) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_1}
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] [Module.FaithfullyFlat R M],
  Subsingleton (TensorProduct R M N) ↔ Subsingleton N

Defined in: Mathlib.RingTheory.Flat.FaithfullyFlat.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module Module.FaithfullyFlat

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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
Module.FaithfullyFlatstatement and proof · cited by 72
Module.FaithfullyFlat.lTensor_reflects_trivialityproof · cited by 3

Cited by2

Results whose statement or proof uses this declaration.

IsBaseChange.map_smul_top_ne_top_iff_of_faithfullyFlatproof · cited by 1
Module.FaithfullyFlat.nontrivial_tensorProduct_iff_rightproof · cited by 0