Theorems · Theorem · commutative algebra
RingHom.quasiFinite_algebraMap
∀ {R : Type u_4} {S : Type u_5} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S],
(algebraMap R S).QuasiFinite ↔ Algebra.QuasiFinite R S- Defined in
- Mathlib.RingTheory.RingHom.QuasiFinite
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Algebra.algebraMapstatement and proof · cited by 4,706
- Algebra.QuasiFinitestatement and proof · cited by 28
- RingHom.QuasiFinitestatement · cited by 21
- toAlgebra_algebraMapproof · cited by 17
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAtproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2
- RingHom.QuasiFinite.holdsForLocalizationAwayproof · cited by 1
- RingHom.QuasiFinite.isStableUnderBaseChangeproof · cited by 1
- RingHom.QuasiFinite.ofLocalizationSpanTargetproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAtproof · cited by 1