Theorems · Theorem · commutative algebra
Ideal.mem_torsionOf_iff
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M) (a : R),
a ∈ Ideal.torsionOf R M x ↔ a • x = 0- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Idealstatement · cited by 4,748
- Ideal.torsionOfstatement · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.torsionOf_eq_bot_iff_of_noZeroSMulDivisorsproof · cited by 0
- Ideal.torsionOf_eq_top_iffproof · cited by 0