Description: The quotient $\mathbb Z[x]/(x^2-1)$ over the integers $\mathbb Z$.

Notes:

Keywords quotient ring polynomial ring

Reference(s):

This ring has the following properties:

The ring lacks the following properties:

algebraically closed field
Artinian
atomic domain
Bezout domain
characteristic 0 field
Dedekind domain
domain
dual
Euclidean domain
Euclidean field
field
Frobenius
GCD domain
Krull domain
local
Mori domain
normal domain
ordered field
perfect
perfect field
principal ideal domain
Prufer domain
pseudo Frobenius
Pythagorean field
quadratically closed field
regular local
Schreier domain
self-injective
semilocal
semiperfect
semiprimary
semisimple
serial
unique factorization domain
valuation
von Neumann regular

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