Theorems · Theorem · commutative algebra
fg_adjoin_of_finite
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {s : Set A},
s.Finite → (∀ x ∈ s, IsIntegral R x) → (Subalgebra.toSubmodule (Algebra.adjoin R s)).FG[Stacks Tag 09GH](https://stacks.math.columbia.edu/tag/09GH)
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Bot.botproof · cited by 4,720
- Set.Finitestatement and proof · cited by 1,814
- Submodule.spanproof · cited by 1,504
- Subalgebrastatement and proof · cited by 1,353
- OrderEmbeddingstatement · cited by 619
- Algebra.adjoinstatement and proof · cited by 535
Cited by9
Results whose statement or proof uses this declaration.
- isIntegral_transproof · cited by 15
- Algebra.IsIntegral.finiteproof · cited by 5
- Polynomial.IsSplittingField.finiteDimensionalproof · cited by 3
- IsCyclotomicExtension.finite_of_singletonproof · cited by 2
- Subalgebra.LinearDisjoint.of_linearDisjoint_finite_leftproof · cited by 2
- isNoetherian_adjoin_finsetproof · cited by 1
- Polynomial.lift_of_splitsproof · cited by 0
- Algebra.finite_adjoin_of_finite_of_isIntegralproof · cited by 0