Theorems · Theorem · commutative algebra
AdjoinRoot.algHom_ext
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] {f : Polynomial R} [inst_1 : Semiring S] [inst_2 : Algebra R S]
{g₁ g₂ : AdjoinRoot f →ₐ[R] S}, g₁ (AdjoinRoot.root f) = g₂ (AdjoinRoot.root f) → g₁ = g₂Two R-AlgHom from AdjoinRoot f to the same R-algebra are the same iff
they agree on root f.
- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- CommRingstatement and proof · cited by 17,173
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement and proof · cited by 3,236
- AdjoinRootstatement and proof · cited by 177
- AdjoinRoot.rootstatement and proof · cited by 77
- Polynomial.algHom_extproof · cited by 19
- Ideal.Quotient.algHom_extproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- AdjoinRoot.liftAlgHom_eq_algHomproof · cited by 0
- AdjoinRoot.algHom_ext_iffproof · cited by 0
- AdjoinRoot.algHom_subsingletonproof · cited by 0