Theorems · Theorem · commutative algebra
AdjoinRoot.aeval_algHom_eq_zero
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] (f : Polynomial R) [inst_1 : CommRing S] [inst_2 : Algebra R S]
(ϕ : AdjoinRoot f →ₐ[R] S), (Polynomial.aeval (ϕ (AdjoinRoot.root f))) f = 0- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- map_zeroproof · cited by 1,614
- RingHom.compproof · cited by 899
- Polynomial.aevalstatement · cited by 615
- AlgHom.toRingHomproof · cited by 490
- Polynomial.eval₂proof · cited by 267
Cited by1
Results whose statement or proof uses this declaration.
- AdjoinRoot.liftAlgHom_eq_algHomstatement and proof · cited by 0