Theorems · Theorem · commutative algebra
Submodule.annihilator_top
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
⊤.annihilator = Module.annihilator R M- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 32 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 · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement · cited by 4,748
- Module.annihilatorstatement · cited by 61
- Submodule.annihilatorstatement · cited by 42
- Submodule.topEquivproof · cited by 16
- LinearEquiv.annihilator_eqproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- Submodule.top_ne_ideal_smul_of_le_jacobson_annihilatorproof · cited by 6
- IsSemisimpleModule.annihilator_isRadicalproof · cited by 4
- Module.mem_support_iff_of_finiteproof · cited by 4
- Submodule.annihilator_quotientproof · cited by 2
- IsSemiprimaryRing.inductionproof · cited by 2
- IsLocalRing.isRegular_iff_isWeaklyRegular_of_subset_maximalIdealproof · cited by 1