mkOfPrimitiveElement — Mathlib

English

The abstract IsAdjoinRootMonic corresponding to a primitive element has monic minimal polynomial; i.e., (minpoly F α).Monic.

Русский

У связанного с примитивным элементом IsAdjoinRootMonic полином минимальный моноичен; то есть (minpoly F α).Monic.

LaTeX

$$(minpoly F α).Monic$$

Lean4

/-- If `α` is primitive in `E/f`, then `E` is given by adjoining a root of `minpoly F α`. -/
abbrev _root_.IsAdjoinRootMonic.mkOfPrimitiveElement {α : E} (hα : IsIntegral F α) (hα₂ : F⟮α⟯ = ⊤) :
    IsAdjoinRootMonic E (minpoly F α)
    where
  __ := IsAdjoinRoot.mkOfPrimitiveElement hα hα₂
  monic := minpoly.monic hα

Похожие утверждения