Theorems · Theorem · commutative algebra
Ideal.exists_disjoint_powers_of_span_eq_top
∀ {α : Type u} [inst : CommSemiring α] (s : Set α),
Ideal.span s = ⊤ → ∀ (I : Ideal α), I ≠ ⊤ → ∃ r ∈ s, Disjoint ↑I ↑(Submonoid.powers r)- Defined in
- Mathlib.RingTheory.Ideal.Maximal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.
- Setstatement and proof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Submonoidstatement · cited by 3,086
- Disjointstatement and proof · cited by 2,201
- Ideal.spanstatement and proof · cited by 948
- Ideal.IsMaximalproof · cited by 452
- Submonoid.powersstatement and proof · cited by 408
- eq_top_iffproof · cited by 236
- Set.disjoint_leftproof · cited by 121
Cited by3
Results whose statement or proof uses this declaration.
- Localization.algebraMap_injective_of_span_eq_topproof · cited by 2
- Module.eq_of_isLocalized_spanproof · cited by 2
- Submodule.mem_of_isLocalized_spanproof · cited by 1