Theorems · Definition · commutative algebra
Algebra.Extension.ker
{R : Type u} →
{S : Type v} →
[inst : CommRing R] → [inst_1 : CommRing S] → [inst_2 : Algebra R S] → (P : Algebra.Extension R S) → Ideal P.RingThe kernel of an extension.
- Defined in
- Mathlib.RingTheory.Extension.Basic
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- RingHom.kerproof · cited by 363
- Algebra.Extension.Ringstatement and proof · cited by 179
- Algebra.Extensionstatement and proof · cited by 138
Cited by89
Results whose statement or proof uses this declaration.
- Algebra.Extension.Cotangentproof · cited by 121
- Algebra.Extension.Cotangent.mkstatement and proof · cited by 49
- Algebra.Generators.kerproof · cited by 46
- Algebra.Extension.Cotangent.mapproof · cited by 40
- Algebra.Extension.Cotangent.valstatement · cited by 29
- Algebra.Extension.Cotangent.mk_surjectivestatement and proof · cited by 22
- Algebra.Extension.Cotangent.extstatement · cited by 15
- Algebra.Extension.H1Cotangent.map_eqproof · cited by 6
- Algebra.Generators.Cotangent.exactproof · cited by 6
- Algebra.Extension.infinitesimalproof · cited by 5
- Algebra.Extension.Cotangent.ofstatement and proof · cited by 5
- Algebra.Extension.Hom.mapKerstatement and proof · cited by 5