Theorems · Theorem · commutative algebra
Algebra.QuasiFinite.of_isIntegral_of_finiteType
∀ {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] [Algebra.IsIntegral R S]
[Algebra.FiniteType R T] (s : S) [IsLocalization.Away s T], Algebra.QuasiFinite R TIf T is both a finite type R-algebra, and the localization of an integral R-algebra
(away from an element), then T is quasi-finite over R
- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites49
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Ringproof · cited by 7,463
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- one_mulproof · cited by 2,841
- Subalgebraproof · cited by 1,353
- MulActionproof · cited by 1,294
- map_mulproof · cited by 1,137
- Module.Finiteproof · cited by 1,032
Cited by1
Results whose statement or proof uses this declaration.
- RingHom.QuasiFinite.of_isIntegral_of_finiteTypeproof · cited by 1