Theorems · Theorem · commutative algebra
Algebra.essFiniteType_iff
∀ (R : Type u_1) (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S], Algebra.EssFiniteType R S ↔ ∃ σ, ∀ (s : S), ∃ t ∈ Algebra.adjoin R ↑σ, IsUnit t ∧ s * t ∈ Algebra.adjoin R ↑σ
- Defined in
- Mathlib.RingTheory.EssentialFiniteness
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finsetstatement and proof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- SetLike.coestatement and proof · cited by 8,199
- Algebra.algebraMapproof · cited by 4,706
- IsUnitstatement · cited by 1,602
- Subalgebrastatement · cited by 1,353
- IsLocalizationproof · cited by 636
- Algebra.adjoinstatement and proof · cited by 535
- Submonoid.comapproof · cited by 179
- Algebra.EssFiniteTypestatement and proof · cited by 68
- IsUnit.submonoidproof · cited by 56
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.EssFiniteType.of_compproof · cited by 8
- Algebra.EssFiniteType.compproof · cited by 7
- Algebra.EssFiniteType.of_isLocalizationproof · cited by 5