Theorems · Theorem · commutative algebra
AdjoinRoot.liftAlgHom_eq_algHom
∀ {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), AdjoinRoot.liftAlgHom f (Algebra.ofId R S) (ϕ (AdjoinRoot.root f)) ⋯ = ϕ- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement and proof · cited by 3,236
- AdjoinRootstatement and proof · cited by 177
- Algebra.ofIdstatement and proof · cited by 166
- AdjoinRoot.rootstatement and proof · cited by 77
- AdjoinRoot.liftAlgHomstatement · cited by 16
- AdjoinRoot.liftAlgHom_rootproof · cited by 8
- AdjoinRoot.algHom_extproof · cited by 3
- AdjoinRoot.aeval_algHom_eq_zerostatement and proof · cited by 1
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