Theorems · Theorem · commutative algebra
Algebra.finite_adjoin_of_finite_of_isIntegral
∀ {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) → Module.Finite R ↥(Algebra.adjoin R s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Finitestatement and proof · cited by 1,814
- Subalgebrastatement · cited by 1,353
- Module.Finitestatement · cited by 1,032
- Algebra.adjoinstatement · cited by 535
- IsIntegralstatement and proof · cited by 427
- Module.Finite.of_fgproof · cited by 21
- fg_adjoin_of_finiteproof · cited by 9
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