spanNorm_bot — Mathlib

English

Under CharZero, the same counting relation holds as in 178013: the number of I with absNorm I ≤ n equals the number of non-zero-divisor I with absNorm ≤ n, plus 1.

Русский

При CharZero то же соотношение счета: число I с absNorm(I) ≤ n равно числу I без нулевых делителей с absNorm ≤ n плюс 1.

LaTeX

$$$$\#\{ I:\mathrm{Ideal}(S) \mid \operatorname{absNorm}(I) \le n \} = \#\{ I:\, I\in (\mathrm{Ideal}(S))^{0} \mid \operatorname{absNorm}(I) \le n \} + 1.$$$$

Lean4

@[simp]
theorem spanNorm_bot : spanNorm R (⊥ : Ideal S) = ⊥ :=
  span_eq_bot.mpr fun x hx => by simpa using hx

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