Theorems · Theorem · commutative algebra
Submodule.annihilator_span_singleton
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (g : M),
(R ∙ g).annihilator = (LinearMap.toSpanSingleton R M g).ker- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingHom.idstatement · cited by 18,349
- 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
- LinearMap.kerstatement and proof · cited by 848
- LinearMap.toSpanSingletonstatement and proof · cited by 78
- Submodule.annihilatorstatement · cited by 42
- ciInf_uniqueproof · cited by 9
- Submodule.annihilator_spanproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.annihilator_span_singleton_eq_torsionOfproof · cited by 1