Theorems · Theorem · commutative algebra
finite_of_finite_type_of_isJacobsonRing
∀ (R : Type u_1) (S : Type u_2) [inst : CommRing R] [inst_1 : Field S] [inst_2 : Algebra R S] [IsJacobsonRing R] [Algebra.FiniteType R S], Module.Finite R S
[Stacks Tag 0CY7](https://stacks.math.columbia.edu/tag/0CY7) (See also https://en.wikipedia.org/wiki/Zariski%27s_lemma.)
- Defined in
- Mathlib.RingTheory.Jacobson.Ring
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- RingHomproof · cited by 10,189
- Fintypeproof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- AlgHomproof · cited by 3,236
- MvPolynomialproof · cited by 2,140
- Module.Finitestatement · cited by 1,032
- AlgHom.toRingHomproof · cited by 490
- Algebra.IsIntegralproof · cited by 224
Cited by4
Results whose statement or proof uses this declaration.
- Module.finite_of_isSemisimpleRingproof · cited by 1
- finite_of_algHom_finiteType_of_isJacobsonRingproof · cited by 1
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpaceproof · cited by 1
- RingHom.finite_iff_finiteType_of_isJacobsonRingproof · cited by 0