Theorems · Theorem · commutative algebra
DualNumber.algHom_ext
∀ {R : Type u_1} {A : Type u_4} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
⦃f g : DualNumber R →ₐ[R] A⦄, f DualNumber.eps = g DualNumber.eps → f = gFor two R-algebra morphisms out of R[ε] to agree, it suffices for them to agree on ε.
- Defined in
- Mathlib.Algebra.DualNumber
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement and proof · cited by 3,236
- one_smulproof · cited by 1,374
- AlgHom.compproof · cited by 501
- LinearMap.ext_ringproof · cited by 152
- DualNumberstatement and proof · cited by 52
- DualNumber.epsstatement and proof · cited by 30
- TrivSqZeroExt.inlAlgHomproof · cited by 17
- Algebra.ext_idproof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- DualNumber.ringHom_extproof · cited by 1
- DualNumber.algHom_ext_iffproof · cited by 0