Theorems · Theorem · commutative algebra
Ideal.iInf_sup_eq_top
∀ {R : Type u} [inst : Semiring R] {I : Ideal R} {ι : Type u_1} {s : Finset ι} {J : ι → Ideal R}
[∀ (i : ι), (J i).IsTwoSided], (∀ i ∈ s, J i ⊔ I = ⊤) → (⨅ i ∈ s, J i) ⊔ I = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
Around this declaration
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- iInfstatement and proof · cited by 1,690
- Ideal.IsTwoSidedstatement and proof · cited by 179
- sup_commproof · cited by 165
- Ideal.sup_iInf_eq_topproof · cited by 5
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