Theorems · Theorem · commutative algebra
Algebra.FiniteType.iff_quotient_freeAlgebra
∀ {R : Type uR} {A : Type uA} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A],
Algebra.FiniteType R A ↔ ∃ s f, Function.Surjective ⇑fAn algebra is finitely generated if and only if it is a quotient of a free algebra whose variables are indexed by a finset.
- Defined in
- Mathlib.RingTheory.FiniteType
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 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.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- 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
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.univproof · cited by 3,945
- AlgHomstatement and proof · cited by 3,236
- Subalgebraproof · cited by 1,353
- Algebra.adjoinproof · cited by 535
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.FiniteType.iff_quotient_freeAlgebra'proof · cited by 0