Theorems · Theorem · commutative algebra
Submodule.annihilator_iSup
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (ι : Sort w)
(f : ι → Submodule R M), (⨆ i, f i).annihilator = ⨅ i, (f i).annihilator- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Submodulestatement and proof · cited by 7,192
- Idealstatement · cited by 4,748
- add_zeroproof · cited by 2,707
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- iInfstatement and proof · cited by 1,690
- smul_zeroproof · cited by 665
- smul_addproof · cited by 263
- le_iSupproof · cited by 207
Cited by2
Results whose statement or proof uses this declaration.
- IsSemisimpleModule.annihilator_isRadicalproof · cited by 4
- Submodule.annihilator_supproof · cited by 0