Theorems · Theorem · commutative algebra
Ideal.iSup_primaryComponent_eq_top
∀ {A : Type u_1} {M : Type u_2} [inst : CommRing A] [inst_1 : AddCommGroup M] [inst_2 : Module A M]
[IsDedekindDomain A], Module.IsTorsion A M → ⨆ P, Ideal.primaryComponent M P.asIdeal = ⊤- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
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
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- AddCommMonoidproof · cited by 12,281
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Fintypeproof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.primaryComponent.map_surjectiveproof · cited by 0