supportDim_quotient_eq_ringKrullDim

English

The Krull dimension of a module is equal to the Krull dimension of the quotient by its annihilator.

Русский

Крull размерность модуля равна крull размерности тождественного деления по аннигилятору.

LaTeX

$$$\operatorname{supportDim}(R,M) = \operatorname{ringKrullDim}(R \;/\; \operatorname{annihilator}(R,M))$$$

Lean4

theorem supportDim_quotient_eq_ringKrullDim (I : Ideal R) : supportDim R (R ⧸ I) = ringKrullDim (R ⧸ I) := by
  rw [supportDim_eq_ringKrullDim_quotient_annihilator, Ideal.annihilator_quotient]

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