Theorems · Theorem · commutative algebra
Module.annihilator_eq_iInf_torsionOf
∀ (R : Type u_1) {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
Module.annihilator R M = ⨅ x, Ideal.torsionOf R M xThe annihilator of a module is the intersection of the torsion ideals of its elements.
- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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- 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
- iInfstatement · cited by 1,690
- Ideal.extproof · cited by 131
- Module.annihilatorstatement · cited by 61
- Ideal.torsionOfstatement and proof · cited by 14
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