Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.finite_of_free
∀ (R : Type u_1) (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Algebra.FormallyUnramified R S] [Algebra.EssFiniteType R S] [Module.Free R S], Module.Finite R S
An unramified free algebra is finitely generated. Iversen I.2.8
- Defined in
- Mathlib.RingTheory.Unramified.Finite
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites92
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Moduleproof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidproof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringproof · cited by 10,911
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Finsuppproof · cited by 5,255
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Equiv.symmproof · cited by 3,681
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.isSeparableproof · cited by 2
- Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRingproof · cited by 1
- Algebra.FormallyEtale.iff_exists_algEquiv_prodproof · cited by 1
- Algebra.FormallyEtale.of_isSeparable_auxproof · cited by 1
- Algebra.FormallyUnramified.isField_quotient_map_maximalIdealproof · cited by 1
- Algebra.Etale.iff_exists_algEquiv_prodproof · cited by 0
- Algebra.IsUnramifiedAt.not_minpoly_sq_dvdproof · cited by 0