I heard $ \Bbb{C}[x,y,z]/((xy-z^2)$ can be regarded as grade ring, but how ?
$ \Bbb{C}[x,y,z]$ can be regarded as graded ring by decomposition$ \Bbb{C}[x,y,z]＝ \bigoplus_{d\geq 0} A_d$, where $A_d＝${all degree d homogeneous polynomial}, $A_d$ clearly satisfies $A_b・A_c⊆A_{b＋c} $ for all $b,c≧0$.
But in the case $ \Bbb{C}[x,y,z]/((xy-z^2)$, I'm having trouble how to decompose $ \Bbb{C}[x,y,z]/((xy-z^2)$ into $\bigoplus_{d\geq 0} A_d$, which satisfies $A_b・A_c⊆A_{b＋c} $ for all $b,c≧0$ ? What can I take as $A_d$ ?