Theorems · Theorem · commutative algebra

Module.FaithfullyFlat.one_tmul_eq_zero_iff

∀ (R : Type u) (M : Type v) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {A : Type u_1}
  [inst_3 : Ring A] [inst_4 : Algebra R A] [Module.FaithfullyFlat R A] (m : M), 1 ⊗ₜ[R] m = 0 ↔ m = 0

If A is a faithfully flat R-algebra, and m is a term of an R-module M, then 1 ⊗ₜ[R] m = 0 if and only if m = 0.

Defined in

Mathlib.RingTheory.Flat.FaithfullyFlat.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingAddCommGroupModuleRingAlgebraModule.FaithfullyFlat