Mathlib Map

Theorems · Theorem · algebraic geometry

Algebra.QuasiFiniteAt.of_weaklyQuasiFiniteAt

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  [Algebra.FiniteType R S] (p : Ideal S) [inst_4 : p.IsPrime] [Algebra.WeaklyQuasiFiniteAt R p],
  Algebra.QuasiFiniteAt R p
Defined in
Mathlib.RingTheory.ZariskisMainTheorem
Cited by
1 results in Mathlib
Foundations
Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraAlgebra.FiniteTypeIdeal.IsPrimeAlgebra.WeaklyQuasiFiniteAt
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.QuasiFiniteAt.of_quasiFiniteAt_residueField · cited by 1QuasiFiniteAt.of_quasiFin…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraIdeal · cited by 4748IdealIdeal.IsPrime · cited by 827Ideal.IsPrimeAlgebra.FiniteType · cited by 84Algebra.FiniteTypeAlgebra.QuasiFiniteAt · cited by 29Algebra.QuasiFiniteAtAlgebra.WeaklyQuasiFiniteAt · cited by 18Algebra.WeaklyQuasiFinite…Algebra.ZariskisMainProperty.of_finiteType_of_weaklyQuasiFiniteAt · cited by 3ZariskisMainProperty.of_f…Algebra.ZariskisMainProperty.quasiFiniteAt · cited by 1ZariskisMainProperty.quas…QuasiFiniteAt.of_weaklyQuasiF…CITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.