Theorems · Definition · commutative algebra
Algebra.EssFiniteType.subalgebra
(R : Type u_1) →
(S : Type u_2) →
[inst : CommRing R] → [inst_1 : CommRing S] → [inst_2 : Algebra R S] → [Algebra.EssFiniteType R S] → Subalgebra R SA choice of a subalgebra of finite type in an essentially of finite type algebra, such that its localization is the whole ring.
- Defined in
- Mathlib.RingTheory.EssentialFiniteness
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SetLike.coeproof · cited by 8,199
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinproof · cited by 535
- Algebra.EssFiniteTypestatement and proof · cited by 68
- Algebra.EssFiniteType.finsetproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.EssFiniteType.submonoidstatement and proof · cited by 4
- IntermediateField.fg_top_iffproof · cited by 2
- Algebra.EssFiniteType.algHom_extproof · cited by 2
- Algebra.EssFiniteType.isNoetherianRingproof · cited by 2
- Algebra.EssFiniteType.adjoin_mem_finsetstatement · cited by 1
- Algebra.essFiniteType_iff_exists_subalgebraproof · cited by 1