Theorems · Definition · commutative algebra
Module.annihilator
(R : Type u_1) → (M : Type u_2) → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [Module R M] → Ideal R
Module.annihilator R M is the ideal of all elements r : R such that r • M = 0.
- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- RingHom.kerproof · cited by 363
- Module.toAddMonoidEndproof · cited by 1
Cited by63
Results whose statement or proof uses this declaration.
- Submodule.annihilatorproof · cited by 42
- Module.mem_annihilatorstatement and proof · cited by 14
- Module.support_eq_zeroLocusstatement · cited by 10
- Submodule.annihilator_topstatement · cited by 7
- Submodule.top_ne_ideal_smul_of_le_jacobson_annihilatorstatement and proof · cited by 6
- IsSemisimpleModule.annihilator_isRadicalstatement · cited by 4
- Module.mem_support_iff_of_finitestatement and proof · cited by 4
- Ideal.annihilator_quotientstatement · cited by 4
- Module.supportDim_self_eq_ringKrullDimproof · cited by 3
- Submodule.top_ne_pointwise_smul_of_mem_jacobson_annihilatorstatement and proof · cited by 3
- Polynomial.span_minpoly_eq_annihilatorstatement and proof · cited by 3
- LinearEquiv.annihilator_eqstatement · cited by 3