Description: polynomial ring over the real numbers mod the ideal generated by $x^2, y^2, xz,yz,z^2-xy$

Notes: Krull dimension 0

Keywords quotient ring polynomial ring

Reference(s):

This ring has the following properties:

The ring lacks the following properties:

algebraically closed field
atomic domain
Bezout domain
characteristic 0 field
Dedekind domain
domain
Euclidean domain
Euclidean field
field
GCD domain
Krull domain
local complete intersection ring
Mori domain
normal
normal domain
ordered field
perfect field
principal ideal domain
principal ideal ring
Prufer domain
Pythagorean field
quadratically closed field
reduced
regular local
Schreier domain
semiprimitive
semisimple
serial
unique factorization domain
valuation
von Neumann regular

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