Theorems · Theorem · commutative algebra
Ideal.span_iUnion
∀ {α : Type u} [inst : Semiring α] {ι : Sort u_1} (s : ι → Set α), Ideal.span (⋃ i, s i) = ⨆ i, Ideal.span (s i)- Defined in
- Mathlib.RingTheory.Ideal.Span
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Semiringstatement and proof · cited by 13,802
- Idealstatement · cited by 4,748
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- Ideal.spanstatement · cited by 948
- Submodule.span_iUnionproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.IsHomogeneous.iSupproof · cited by 1
- Ideal.toIdeal_homogeneousHull_eq_iSupproof · cited by 1
- Ideal.span_range_eq_iSupproof · cited by 0