Theorems · Theorem · commutative algebra

Module.isTrivialRelation_iff_vanishesTrivially

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {ι : Type u_3}
  [inst_3 : Fintype ι] {f : ι → R} {x : ι → M}, Module.IsTrivialRelation f x ↔ TensorProduct.VanishesTrivially R f x

Module.IsTrivialRelation is equivalent to the predicate TensorProduct.VanishesTrivially defined in Mathlib/LinearAlgebra/TensorProduct/Vanishing.lean.

Defined in

Mathlib.RingTheory.Flat.EquationalCriterion

Cited by

1 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleFintype