Theorems · Theorem · commutative algebra

Submodule.exists_isTorsionBy

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : (x : M) → Decidable (x = 0)] {p : R} (hM : Module.IsTorsion' M ↥(Submonoid.powers p)) (d : ℕ),
  d ≠ 0 →
    ∀ (s : Fin d → M), Submodule.span R (Set.range s) = ⊤ → ∃ j, Module.IsTorsionBy R M (p ^ Submodule.pOrder hM (s j))

Defined in

Mathlib.Algebra.Module.Torsion.Basic

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleDecidable