Theorems · Theorem · commutative algebra
RingHom.finiteType_algebraMap
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B],
(algebraMap A B).FiniteType ↔ Algebra.FiniteType A B- Defined in
- Mathlib.RingTheory.FiniteType
- Cited by
- 5 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.FiniteTypestatement and proof · cited by 84
- RingHom.FiniteTypestatement · cited by 46
- toAlgebra_algebraMapproof · cited by 17
Cited by5
Results whose statement or proof uses this declaration.
- RingHom.finiteType_holdsForLocalizationAwayproof · cited by 1
- RingHom.finiteType_isStableUnderBaseChangeproof · cited by 1
- Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐproof · cited by 1
- RingHom.FiniteType.codescendsAlong_faithfullyFlatproof · cited by 0
- exists_finite_inj_algHom_of_fgproof · cited by 0