algebraMap_quotient_of_ramificationIdx_neZero

English

Under an algebra isomorphism e: S ≃ A, inertiaDeg p (P.comap e) = inertiaDeg p P; inertia degree is preserved by comap with respect to an equivalence.

Русский

При эквиваленте алгебр сохраняется inertiaDeg при comap: inertiaDeg(p, P.comap e) = inertiaDeg(p, P).

LaTeX

$$$\\\\operatorname{inertiaDeg} \\, p \\, (P^{\\\\comap e}) = \\,\\\\operatorname{inertiaDeg} \\, p \\, P$$$

Lean4

@[simp]
theorem algebraMap_quotient_of_ramificationIdx_neZero [NeZero e] (x : R) :
    algebraMap (R ⧸ p) (S ⧸ P) (Ideal.Quotient.mk p x) = Ideal.Quotient.mk P (f x) :=
  rfl

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