Theorems · Theorem · commutative algebra
Module.annihilator_eq_top_iff
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
Module.annihilator R M = ⊤ ↔ Subsingleton M- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Top.topstatement and proof · cited by 9,680
- Idealstatement · cited by 4,748
- one_smulproof · cited by 1,374
- top_le_iffproof · cited by 175
- Module.annihilatorstatement and proof · cited by 61
- Submodule.mem_topproof · cited by 58
- Module.mem_annihilatorproof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.annihilator_eq_top_iffproof · cited by 2
- Module.exists_ker_toSpanSingleton_eq_annihilatorproof · cited by 0