Ring $R_{ 214 }$

Description:

Let $K$ be a field and $X_1, X_2, \ldots$ be indeterminates over $K$. Let $R_0 = K[X_1, X_2, \ldots] / (\{X_n(X_{n-1} - X_n) \mid n \geq 2\})$. Let $x_n$ denote the image of $X_n$ in $R_0$. Let $R$ be the localization of $R_0$ at the ideal $(x_1, x_2, \ldots)$.

Keywords localization polynomial ring quotient ring