English
If I,J come from coe-ideals I',J', then mk I = mk J iff there exist x,y in R with nonzero such that span{x}·I' = span{y}·J'.
Русский
Если I,J получены из коерциированных идеалов I', J', тогда mk I = mk J тогда, когда существуют x,y ∈ R с не нулем, удовлетворяющее равенству: span{x}·I' = span{y}·J'.
LaTeX
$$$\mathrm{ClassGroup.mk0}(\langle I',hI\rangle) = \mathrm{ClassGroup.mk0}(\langle J',hJ\rangle) \iff \exists x,y\in R, x\neq 0\land y\neq 0 \land \mathrm{Ideal.span}\{x\}\cdot I' = \mathrm{Ideal.span}\{y\}\cdot J'.$$$
Lean4
/-- Send a nonzero ideal to the corresponding class in the class group. -/
noncomputable def mk0 [IsDedekindDomain R] : (Ideal R)⁰ →* ClassGroup R :=
ClassGroup.mk.comp (FractionalIdeal.mk0 (FractionRing R))
