Theorems · Definition · commutative algebra

AdjoinRoot.liftAlgHom

{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) → Polynomial.eval₂ (↑i) x p = 0 → AdjoinRoot p →ₐ[S] T

Produce an algebra homomorphism AdjoinRoot f →ₐ[R] S sending root f to a root of f in S.

Defined in

Mathlib.RingTheory.AdjoinRoot

Cited by

16 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebra