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Theorems · Definition · commutative algebra

RingHom.FiniteType

{A : Type u_1} → {B : Type u_2} → [inst : CommRing A] → [inst_1 : CommRing B] → (A →+* B) → Prop

A ring morphism A →+* B is of FiniteType if B is finitely generated as A-algebra.

Defined in
Mathlib.RingTheory.FiniteType
Cited by
46 results in Mathlib
Foundations
Depth 19 from the axioms · uses no axioms
Assumes
CommRingCommRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgHom.FiniteType · cited by 9AlgHom.FiniteTypeAlgebraicGeometry.Scheme.Hom.finiteType_appLE · cited by 6Hom.finiteType_appLERingHom.finiteType_algebraMap · cited by 5RingHom.finiteType_algebr…RingHom.FiniteType.essFiniteType · cited by 4FiniteType.essFiniteTypeRingHom.IsIntegral.to_finite · cited by 4IsIntegral.to_finiteRingHom.finiteType_respectsIso · cited by 4RingHom.finiteType_respec…RingHom.FiniteType.comp · cited by 3FiniteType.compRingHom.FiniteType.of_comp_finiteType · cited by 3FiniteType.of_comp_finite…RingHom.FiniteType.of_finitePresentation · cited by 3FiniteType.of_finitePrese…RingHom.FiniteType.of_surjective · cited by 3FiniteType.of_surjectiveAlgebraicGeometry.LocallyOfFiniteType.isLocallyNoetherian · cited by 2LocallyOfFiniteType.isLoc…AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpace · cited by 2LocallyOfFiniteType.jacob…RingHom.Finite.finiteType · cited by 2Finite.finiteTypeRingHom.FiniteType.comp_surjective · cited by 2FiniteType.comp_surjectiveRingHom.FiniteType.id · cited by 2FiniteType.idCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomAlgebra.FiniteType · cited by 84Algebra.FiniteTypeRingHom.FiniteTypeCITED BYCITES

Cites3

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Cited by50

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