Theorems · Theorem · commutative algebra
Algebra.QuasiFiniteAt.of_isOpen_singleton
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsArtinianRing R]
(p : PrimeSpectrum S) [Algebra.FiniteType R S], IsOpen {p} → Algebra.QuasiFiniteAt R p.asIdeal- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites65
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
- CommSemiringproof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- mul_oneproof · cited by 3,885
- AlgHomproof · cited by 3,236
- IsOpenstatement and proof · cited by 2,400
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.QuasiFiniteAt.of_isOpen_singleton_fiberproof · cited by 1