Theorems · Theorem · commutative algebra
Algebra.QuasiFiniteAt.exists_basicOpen_eq_singleton
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal S)
[inst_3 : p.IsPrime] [IsArtinianRing R] [Algebra.EssFiniteType R S] [Algebra.QuasiFiniteAt R p],
∃ f ∉ p, ↑(PrimeSpectrum.basicOpen f) = {{ asIdeal := p, isPrime := inst_3 }}- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites60
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 · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgEquivproof · cited by 1,681
- one_smulproof · cited by 1,374
- Module.Finiteproof · cited by 1,032
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.QuasiFiniteAt.isClopen_singletonproof · cited by 2
- Ideal.exists_not_mem_forall_mem_of_ne_of_liesOverproof · cited by 1