equivAdjoinSimple — Mathlib

English

If y is algebraic over K and aeval y on minpoly K x vanishes, then minpoly K y = minpoly K x.

Русский

Если y алгебраически над K и aeval y по minpoly K x обнуляется, тогда minpoly K y = minpoly K x.

LaTeX

$$minpoly.eq_of_root hx h_ev$$

Lean4

/-- `pb.equivAdjoinSimple` is the equivalence between `K⟮pb.gen⟯` and `L` itself. -/
noncomputable def equivAdjoinSimple (pb : PowerBasis K L) : K⟮pb.gen⟯ ≃ₐ[K] L :=
  (adjoin.powerBasis pb.isIntegral_gen).equivOfMinpoly pb <| by rw [adjoin.powerBasis_gen, minpoly_gen]

Похожие утверждения