Theorems · Theorem · commutative algebra
Module.Finite.of_quasiFinite
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsArtinianRing R]
[Algebra.QuasiFinite R S], Module.Finite R S- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fintypeproof · cited by 7,736
- TensorProductproof · cited by 2,545
- AlgEquivproof · cited by 1,681
- Module.Finitestatement and proof · cited by 1,032
- PrimeSpectrumproof · cited by 625
- AlgEquiv.symmproof · cited by 615
- Ideal.primeComplproof · cited by 462
- PrimeSpectrum.asIdealproof · cited by 333
- Localization.AtPrimeproof · cited by 299
- Localizationproof · cited by 270
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.QuasiFinite.of_restrictScalarsproof · cited by 3
- AlgebraicGeometry.IsLocallyArtinian.of_locallyQuasiFiniteproof · cited by 2
- Algebra.QuasiFiniteAt.exists_basicOpen_eq_singletonproof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- Algebra.QuasiFinite.iff_of_isArtinianRingproof · cited by 1
- AlgebraicGeometry.IsFinite.of_locallyQuasiFiniteproof · cited by 0
- Algebra.WeaklyQuasiFiniteAt.finite_locoalizationproof · cited by 0