Theorems · Theorem · field theory

minpoly.aeval_algHom

∀ (A : Type u_1) {B : Type u_2} {B' : Type u_3} [inst : CommRing A] [inst_1 : Ring B] [inst_2 : Ring B']
  [inst_3 : Algebra A B] [inst_4 : Algebra A B'] (f : B →ₐ[A] B') (x : B), (Polynomial.aeval (f x)) (minpoly A x) = 0

Given any f : B →ₐ[A] B' and any x : L, the minimal polynomial of x vanishes at f x.

Defined in

Mathlib.FieldTheory.Minpoly.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingRingRingAlgebraAlgebra