*This ring suggested by: Watson*

Description: $\Bbb Q[X,Y]$ localized at the prime ideal $(X,Y)$.

Notes: A local ring with an infinite prime spectrum. It has Krull dimension $2$.

Keywords localization polynomial ring

Reference(s):

This ring has the following properties:

The ring lacks the following properties:

algebraically closed field
Artinian
Bezout domain
Bezout ring
characteristic 0 field
Dedekind domain
distributive
dual
Euclidean domain
Euclidean field
field
finite
Frobenius
Kasch
ordered field
perfect
perfect field
principal ideal domain
principal ideal ring
Prufer domain
pseudo Frobenius
Pythagorean field
quadratically closed field
self-injective
semiprimary
semisimple
serial
valuation
von Neumann regular

We don't know if the ring has or lacks the following properties: