Theorems · Definition · commutative algebra

IsAdjoinRoot.ofAlgEquiv

{R : Type u} →
  {S : Type v} →
    [inst : CommRing R] →
      [inst_1 : Ring S] →
        {f : Polynomial R} →
          [inst_2 : Algebra R S] →
            IsAdjoinRoot S f →
              {T : Type u_1} → [inst_3 : Ring T] → [inst_4 : Algebra R T] → (S ≃ₐ[R] T) → IsAdjoinRoot T f

Transfer IsAdjoinRoot across an algebra isomorphism. This is the converse of IsAdjoinRoot.algEquiv: this turns an AlgEquiv into an IsAdjoinRoot, and IsAdjoinRoot.algEquiv turns an IsAdjoinRoot into an AlgEquiv.

Defined in

Mathlib.RingTheory.IsAdjoinRoot

Cited by

4 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingRingAlgebraRingAlgebra