Theorems · Theorem · commutative algebra
AdjoinRoot.liftAlgHom_root
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
[inst_3 : Algebra S R] [inst_4 : Algebra S T] (p : Polynomial R) (i : R →ₐ[S] T) (x : T)
(h : Polynomial.eval₂ (↑i) x p = 0), (AdjoinRoot.liftAlgHom p i x h) (AdjoinRoot.root p) = x- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- RingHomClass.toRingHomstatement and proof · cited by 746
- Polynomial.eval₂statement and proof · cited by 267
- AdjoinRootstatement · cited by 177
- AdjoinRoot.rootstatement · cited by 77
- AdjoinRoot.liftAlgHomstatement · cited by 16
- AdjoinRoot.lift_rootproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- Algebra.adjoin.powerBasis'_genproof · cited by 5
- Field.nonempty_algHom_of_exists_rootproof · cited by 3
- adjoinRootXPowSubCEquiv_rootproof · cited by 2
- autAdjoinRootXPowSubC_rootproof · cited by 1
- Module.Finite.exists_free_surjectiveproof · cited by 1
- AdjoinRoot.Minpoly.toAdjoin.surjectiveproof · cited by 0
- AdjoinRoot.liftAlgHom_eq_algHomproof · cited by 0
- AdjoinRoot.Minpoly.coe_toAdjoin_mk_Xproof · cited by 0