vanishingIdeal_zeroLocus — Mathlib

English

The vanishing ideal of a singleton is prime, and earlier results imply related prime properties.

Русский

Нулевой идеал синглтона прост

LaTeX

$$IsPrime vanishingIdealSingleton$$

Lean4

@[simp high] -- This needs to fire before `vanishingIdeal_zeroLocus_eq_radical`

theorem vanishingIdeal_zeroLocus (P : Ideal (MvPolynomial σ k)) [h : P.IsPrime] :
    vanishingIdeal k (zeroLocus K P) = P :=
  Trans.trans (vanishingIdeal_zeroLocus_eq_radical P) h.radical

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