Theorems · Theorem · commutative algebra
Subalgebra.fg_def
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {S : Subalgebra R A},
S.FG ↔ ∃ t, t.Finite ∧ Algebra.adjoin R t = S- Defined in
- Mathlib.RingTheory.Adjoin.FG
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 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.
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Set.Finitestatement · cited by 1,814
- Subalgebrastatement and proof · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- Subalgebra.FGstatement · cited by 45
- Set.exists_finite_iff_finsetproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- Subalgebra.FG.supproof · cited by 2
- is_noetherian_subring_closureproof · cited by 0
- Subalgebra.FG.prodproof · cited by 0