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

- T. S. Shores and R. Wiegand. Rings whose finitely generated modules are direct sums of cyclics. (1974) @ Example 4.4 p 166

Known Properties

Legend

- = has the property
- = does not have the property
- = information not in database

(Nothing was retrieved.)

Name | Description |
---|---|

Idempotents | $\{0,1\}$ |

Left singular ideal | $\{0\}$ |

Left socle | $\{0\}$ |

Nilpotents | $\{0\}$ |

Right singular ideal | $\{0\}$ |

Right socle | $\{0\}$ |

Zero divisors | $\{0\}$ |