Theorems · Theorem · commutative algebra
Ideal.span_eq_top_iff_finite
∀ {α : Type u} [inst : Semiring α] (s : Set α), Ideal.span s = ⊤ ↔ ∃ s', ↑s' ⊆ s ∧ Ideal.span ↑s' = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Span
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 67 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.
Cites9
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
- Finsetstatement and proof · cited by 13,712
- Top.topstatement · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement · cited by 4,748
- Ideal.spanstatement and proof · cited by 948
- Ideal.span_monoproof · cited by 16
- Submodule.mem_span_finite_of_mem_spanproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- Module.Finite.of_localizationSpan'proof · cited by 4
- AlgebraicGeometry.of_affine_open_coverproof · cited by 3
- Algebra.FiniteType.of_span_eq_top_targetproof · cited by 2
- AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpenproof · cited by 2
- RingHom.locally_iff_finiteproof · cited by 2
- Algebra.FinitePresentation.of_span_eq_top_targetproof · cited by 2
- RingHom.ofLocalizationSpanTarget_iff_finiteproof · cited by 1
- RingHom.ofLocalizationSpan_iff_finiteproof · cited by 1
- Algebra.FiniteType.of_span_eq_top_sourceproof · cited by 1
- CommRingCat.essentiallySmall_of_localizationAwayproof · cited by 1