Theorems · Theorem · commutative algebra

Module.isTorsionBy_iff_torsionBy_eq_top

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (a : R),
  Module.IsTorsionBy R M a ↔ Submodule.torsionBy R M a = ⊤

An a-torsion module is a module whose a-torsion submodule is the full space.

Defined in

Mathlib.Algebra.Module.Torsion.Basic

Cited by

2 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModule