Theorems · Theorem · commutative algebra
Subalgebra.fg_iff_finiteType
∀ {R : Type uR} {A : Type uA} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (S : Subalgebra R A),
S.FG ↔ Algebra.FiniteType R ↥S- Defined in
- Mathlib.RingTheory.FiniteType
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Top.topproof · cited by 9,680
- Subalgebrastatement and proof · cited by 1,353
- Algebra.FiniteTypestatement and proof · cited by 84
- Subalgebra.FGstatement and proof · cited by 45
- Algebra.FiniteType.outproof · cited by 14
- Subalgebra.fg_topproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.FiniteType.adjoin_of_finiteproof · cited by 1
- Algebra.Smooth.exists_subalgebra_finiteTypeproof · cited by 0