Zu einer affin-algebraischen Menge V ⊆ A K n {\displaystyle {}V\subseteq {{\mathbb {A} }_{K}^{n}}} mit Verschwindungsideal Id ( V ) {\displaystyle {}\operatorname {Id} \,(V)} nennt man R ( V ) = K [ X 1 , … , X n ] / Id ( V ) {\displaystyle {}R(V)=K[X_{1},\ldots ,X_{n}]/\operatorname {Id} \,(V)} den Koordinatenring von V {\displaystyle {}V} .
![{\displaystyle {}R(V)=K[X_{1},\ldots ,X_{n}]/\operatorname {Id} \,(V)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f6e7ef768a8d088ecd9ef0a88f08b41fdcbdfba9)
