Description: The quotient ring $F_2[x,y]/(x,y)^2$ for the field $F_2$ of two elements.

Notes: Lattice of proper ideals is the diamond lattice. All ideals principal except for maximal ideal. Zero Krull dimension

Keywords quotient 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
distributive
domain
dual
Euclidean domain
Euclidean field
field
Frobenius
GCD domain
Gorenstein
Krull domain
local complete intersection ring
Mori domain
normal
normal domain
ordered field
perfect field
principal ideal domain
principal ideal ring
Prufer domain
pseudo Frobenius
Pythagorean field
quadratically closed field
reduced
regular
regular local
Schreier domain
self-injective
semiprimitive
semisimple
serial
unique factorization domain
valuation
von Neumann regular

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