Ring $R_{ 131 }$

Description:

Let $x_i$ be countably many indeterminates, and $T=\mathbb Q[\{x_i^2\mid i \in \mathbb N\}\cup\{x_i^3\in\mathbb N\}]$. Let $S_0$ be the multiplicative set that is the intersection of complements of $(x_i^2, x_i^3)$ in $\mathbb Q[\{x_i\mid i \in \mathbb N\}]$, and $S=S_0\cap T$. The desired ring is the localization $TS^{-1}$

Notes: not integrally closed in its field of fractions

Keywords localization polynomial ring