Theorems · Theorem · commutative algebra
Algebra.FiniteType.of_span_eq_top_target
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (s : Set S),
Ideal.span s = ⊤ → (∀ x ∈ s, Algebra.FiniteType R (Localization.Away x)) → Algebra.FiniteType R SFinite-type can be checked on a standard covering of the target.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Finsuppproof · cited by 5,255
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Submonoidproof · cited by 3,086
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.FinitePresentation.of_span_eq_top_targetproof · cited by 2
- RingHom.finiteType_ofLocalizationSpanTargetproof · cited by 1