Theorems · Theorem · field theory

minpoly.eq_X_sub_C_of_algebraMap_inj

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : Ring B] [inst_2 : Algebra A B] (a : A),
  Function.Injective ⇑(algebraMap A B) → minpoly A ((algebraMap A B) a) = Polynomial.X - Polynomial.C a

If B/A is an injective ring extension, and a is an element of A, then the minimal polynomial of algebraMap A B a is X - C a.

Defined in

Mathlib.FieldTheory.Minpoly.Basic

Cited by

4 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingRingAlgebra