supp_quot — Mathlib

English

The quotient valuation has support equal to the image of the original support under the quotient map.

Русский

Опора кватирования равна образу опоры исходной оценки через тождество факторизации.

LaTeX

$$$\\mathrm{supp}(\\mathrm{Valuation.onQuot}(v)) = (\\mathrm{supp}(v)).map(\\mathrm{Ideal.Quotient.mk}\, J)$$$

Lean4

/-- The quotient valuation on `R / J` has support `(supp v) / J` if `J ⊆ supp v`. -/
theorem supp_quot {J : Ideal R} (hJ : J ≤ supp v) : supp (v.onQuot hJ) = (supp v).map (Ideal.Quotient.mk J) :=
  Valuation.supp_quot v hJ

Похожие утверждения