Theorems · Theorem · commutative algebra
Subalgebra.fg_adjoin_finset
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (s : Finset A),
(Algebra.adjoin R ↑s).FG- Defined in
- Mathlib.RingTheory.Adjoin.FG
- Cited by
- 5 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.
Cites7
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
- Finsetstatement and proof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- Algebra.adjoinstatement · cited by 535
- Subalgebra.FGstatement · cited by 45
Cited by5
Results whose statement or proof uses this declaration.
- TensorProduct.Algebra.exists_of_fgproof · cited by 3
- exists_fg_and_mem_baseChangeproof · cited by 2
- TensorProduct.Algebra.eq_of_fg_of_subtype_eqproof · cited by 2
- exists_subalgebra_of_fgproof · cited by 1
- PolynomialLaw.exists_lift'proof · cited by 0