Theorems · Theorem · commutative algebra
Subalgebra.FG.sup
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
{S S' : Subalgebra R A}, S.FG → S'.FG → (S ⊔ S').FG- Defined in
- Mathlib.RingTheory.Adjoin.FG
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · 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.Finiteproof · cited by 1,814
- Subalgebrastatement and proof · cited by 1,353
- Algebra.adjoinproof · cited by 535
- Set.Finite.unionproof · cited by 74
- Subalgebra.FGstatement and proof · cited by 45
- Algebra.adjoin_unionproof · cited by 7
- Subalgebra.fg_defproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- TensorProduct.Algebra.eq_of_fg_of_subtype_eq'proof · cited by 1
- PolynomialLaw.exists_lift'proof · cited by 0