Theorems · Theorem · commutative algebra
Algebra.EssFiniteType.adjoin_mem_finset
∀ (R : Type u_1) (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : Algebra.EssFiniteType R S], Algebra.adjoin R {x | ↑x ∈ Algebra.EssFiniteType.finset R S} = ⊤- Defined in
- Mathlib.RingTheory.EssentialFiniteness
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- Top.topstatement · cited by 9,680
- Set.ofPredstatement · cited by 6,101
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- Algebra.EssFiniteTypestatement and proof · cited by 68
- Algebra.EssFiniteType.subalgebrastatement · cited by 5
- Algebra.EssFiniteType.finsetstatement · cited by 5
- Algebra.adjoin_adjoin_coe_preimageproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.EssFiniteType.algHom_extproof · cited by 2