Description: For a field $k$, the formal power series using $x^2$ and $x^3$.

Notes: There are no prime elements. Krull dimension $1$.

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
dual
Euclidean domain
Euclidean field
field
finite
Frobenius
GCD domain
Kasch
ordered field
perfect
perfect field
principal ideal domain
principal ideal ring
pseudo Frobenius
Pythagorean field
quadratically closed field
regular local
Schreier domain
self-injective
semiprimary
semisimple
serial
unique factorization domain
valuation
von Neumann regular

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