Theorems · Definition · commutative algebra
Algebra.Extension.defaultHom
(R : Type u) →
(S : Type v) →
[inst : CommRing R] →
[inst_1 : CommRing S] →
[inst_2 : Algebra R S] → (P : Algebra.Extension R S) → (Algebra.Generators.self R S).toExtension.Hom PThe canonical homomorphism of extensions from the universal extension R[S] → S
(given by Generators.self R S) to any extension P defined via the designated section P.σ.
- Defined in
- Mathlib.RingTheory.Extension.Generators
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MvPolynomial.aevalproof · cited by 298
- Algebra.Extensionstatement and proof · cited by 138
- Algebra.Generators.toExtensionstatement · cited by 103
- Algebra.Extension.Homstatement · cited by 51
- Algebra.Generators.selfstatement · cited by 22
- Algebra.Extension.σproof · cited by 15
- Algebra.Extension.Hom.ofAlgHomproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.Extension.h1CotangentExtendScalarsEquivproof · cited by 3
- Algebra.Extension.h1CotangentEquivCotangent_comp_mapstatement and proof · cited by 1
- Algebra.Extension.h1CotangentExtendScalarsEquiv_symm_toLinearMapstatement · cited by 1
- Algebra.Extension.defaultHom_toRingHom_applystatement and proof · cited by 0
- Algebra.Extension.H1Cotangent.map_defaultHom_surjectivestatement and proof · cited by 0