Theorems · Theorem · commutative algebra
Algebra.QuasiFinite.of_isLocalization
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
[inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T] (M : Submonoid S)
[IsLocalization M T] [Algebra.QuasiFinite R S], Algebra.QuasiFinite R T- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- Algebra.QuasiFinitestatement and proof · cited by 28
- Algebra.QuasiFinite.transproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- RingHom.QuasiFinite.holdsForLocalizationAwayproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAtproof · cited by 1
- Algebra.QuasiFinite.of_isIntegral_of_finiteTypeproof · cited by 1