Theorems · Definition · commutative algebra
RingHom.QuasiFinite
{R : Type u_4} → {S : Type u_5} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → PropA ring hom R →+* S is quasi-finite if S is a quasi-finite R-algebra.
- Defined in
- Mathlib.RingTheory.RingHom.QuasiFinite
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- RingHomstatement and proof · cited by 10,189
- Algebra.QuasiFiniteproof · cited by 28
Cited by24
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAtproof · cited by 14
- RingHom.quasiFinite_algebraMapstatement · cited by 7
- RingHom.QuasiFinite.compstatement and proof · cited by 4
- RingHom.QuasiFinite.of_compstatement and proof · cited by 4
- RingHom.QuasiFinite.respectsIsostatement · cited by 4
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersionproof · cited by 3
- RingHom.QuasiFinite.of_finitestatement · cited by 2
- RingHom.QuasiFinite.stableUnderCompositionstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAtproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iffproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAtproof · cited by 1
- AlgebraicGeometry.LocallyQuasiFinite.casesOnstatement and proof · cited by 1