Theorems · Definition · commutative algebra
Algebra.Generators.Ring
{R : Type u} →
{S : Type v} →
{ι : Type w} →
[inst : CommRing R] → [inst_1 : CommRing S] → [inst_2 : Algebra R S] → Algebra.Generators R S ι → Type (max w u)The polynomial ring w.r.t. a family of generators.
- Defined in
- Mathlib.RingTheory.Extension.Generators
- Cited by
- 133 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 130 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- MvPolynomialproof · cited by 2,140
- Algebra.Generatorsstatement and proof · cited by 152
Cited by162
Results whose statement or proof uses this declaration.
- Algebra.Generators.toExtensionproof · cited by 103
- Algebra.Presentation.relationstatement · cited by 49
- Algebra.Generators.kerstatement · cited by 46
- Algebra.Generators.algebraMap_applystatement and proof · cited by 32
- Algebra.PreSubmersivePresentation.jacobianproof · cited by 31
- Algebra.Generators.Hom.toAlgHomstatement · cited by 30
- Algebra.Generators.σstatement · cited by 29
- Algebra.Generators.Hom.valstatement · cited by 23
- Algebra.PreSubmersivePresentation.jacobiMatrixstatement · cited by 21
- Algebra.Generators.ker_eq_ker_aeval_valstatement · cited by 13
- Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_detstatement and proof · cited by 12
- Algebra.Generators.Hom.toAlgHom_Xstatement · cited by 12