Ring $R_{ 212 }$

Description:

Let $K$ be a field and $\{X_n : n \geq 0\}$, $\{Y_n : n \geq 0\}$ be sets of indeterminates over $K$. Let $I = (\{X_k(Y_n - 1) \mid n \geq k\})\lhd K[X, Y]$. Let $R_0 = K[X, Y] / I$, and let $x_n, y_n$ denote the images of $X_n, Y_n$ in $R_0$. Let $M$ be the ideal of $R_0$ generated by all $x_n$ and all $y_n$, and $Q$ be the ideal of $R_0$ generated by all $x_n$ and all $y_n - 1$. Let $R$ be the localization of $R_0$ at the set $R_0 \setminus (M \cup Q)$.

Keywords localization polynomial ring quotient ring