Ring $R_{ 144 }$

Description:

Start with the ring of power series of the form $\sum a_\alpha x^\alpha$ where $a_\alpha\in \mathbb C$ and $\alpha$ ranges over a well-founded set of nonnegative rationals. Within the field of fractions of this ring, it can be shown there are $n$-pairwise independent maximal valuation rings $D_i$. The ring is $R=\cap_{i=1}^n D_i$. For this ring we use $n=2$.

Notes: This construction produces a ring with $n$ maximal ideals

Keywords power series ring valuations