Theorems · Theorem · commutative algebra

Module.isTorsionBySet_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)
  (s : Set R), Module.IsTorsionBySet R (M ⧸ N) s ↔ ∀ (x : M), ∀ r ∈ s, r • x ∈ N

Defined in

Mathlib.Algebra.Module.Torsion.Basic

Cited by

4 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModule