Theorems · Theorem · commutative algebra

Module.isTorsionBy_quotient_iff

∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (N : Submodule R M)
  (r : R), Module.IsTorsionBy R (M ⧸ N) r ↔ ∀ (x : M), r • x ∈ N

Defined in

Mathlib.Algebra.Module.Torsion.Basic

Cited by

2 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModule