English
The relative norm is a multiplicative map from ideals of S to ideals of R, defined by relNorm(I) = spanNorm_R(I).
Русский
Относительная норма — это умножимообразная отображение идеалов слоя S в идеалы R, задаваемое как relNorm(I) = spanNorm_R(I).
LaTeX
$$$\mathrm{relNorm}: \mathrm{Idl}(S) \to \mathrm{Idl}(R), \quad \mathrm{relNorm}(I) = \mathrm{span}_R(I).$$$
Lean4
/-- The relative norm `Ideal.relNorm R (I : Ideal S)`, where `R` and `S` are Dedekind domains,
and `S` is an extension of `R` that is finite and free as a module. -/
noncomputable def relNorm : Ideal S →*₀ Ideal R
where
toFun := spanNorm R
map_zero' := spanNorm_bot R
map_one' := by rw [one_eq_top, spanNorm_top R, one_eq_top]
map_mul' := spanNorm_mul R
