Theorems · Theorem · commutative algebra
Algebra.QuasiFinite.trans
∀ (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.QuasiFinite R S] [Algebra.QuasiFinite S T], Algebra.QuasiFinite R T
[Stacks Tag 00PO](https://stacks.math.columbia.edu/tag/00PO)
- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Idealproof · cited by 4,748
- IsScalarTowerstatement and proof · cited by 3,896
- TensorProductproof · cited by 2,545
- AlgEquivproof · cited by 1,681
- one_smulproof · cited by 1,374
- TensorProduct.tmulproof · cited by 1,182
- Module.Finiteproof · cited by 1,032
- Ideal.IsPrimeproof · cited by 827
- Ideal.ResidueFieldproof · cited by 119
Cited by8
Results whose statement or proof uses this declaration.
- Algebra.QuasiFinite.of_surjective_algHomproof · cited by 7
- RingHom.QuasiFinite.compproof · cited by 4
- Algebra.QuasiFinite.of_isLocalizationproof · cited by 4
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2
- Algebra.WeaklyQuasiFiniteAt.baseChangeproof · cited by 2
- Algebra.ZariskisMainProperty.quasiFiniteAtproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_quasiFiniteAt_residueFieldproof · cited by 1
- Algebra.QuasiFinite.of_isIntegral_of_finiteTypeproof · cited by 1