Theorems · Theorem · commutative algebra
Ideal.annihilator_span_singleton_eq_torsionOf
∀ {R : Type u_3} {M : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M),
(R ∙ x).annihilator = Ideal.torsionOf R M x- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement · cited by 4,748
- Submodule.spanstatement · cited by 1,504
- Submodule.annihilatorstatement · cited by 42
- Ideal.torsionOfstatement · cited by 14
- Submodule.annihilator_span_singletonproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.iff_exists_tensorProductproof · cited by 2