Description: The quotient of the integers by an ideal $(n)$ where $n>1$ is divisible by at least two different primes, and $n$ isn't squarefree

Notes:

Keywords quotient ring

Reference(s):

This ring has the following properties:

$\pi$-regular
2-primal
Abelian
ACC annihilator (left)
ACC annihilator (right)
ACC principal (left)
ACC principal (right)
Artinian (left)
Artinian (right)
clean
cogenerator ring (left)
cogenerator ring (right)
coherent (left)
coherent (right)
cohopfian (left)
cohopfian (right)
commutative
continuous (left)
continuous (right)
DCC annihilator (left)
DCC annihilator (right)
Dedekind finite
dual (left)
dual (right)
duo (left)
duo (right)
essential socle (left)
essential socle (right)
exchange
FI-injective (left)
FI-injective (right)
finite uniform dimension (left)
finite uniform dimension (right)
finitely cogenerated (left)
finitely cogenerated (right)
finitely generated socle (left)
finitely generated socle (right)
finitely pseudo-Frobenius (left)
finitely pseudo-Frobenius (right)
Frobenius
Goldie (left)
Goldie (right)
I_0
IBN
Kasch (left)
Kasch (right)
lift/rad
nil radical
nilpotent radical
Noetherian (left)
Noetherian (right)
nonzero socle (left)
nonzero socle (right)
Ore ring (left)
Ore ring (right)
orthogonally finite
perfect (left)
perfect (right)
polynomial identity
principally injective (left)
principally injective (right)
pseudo-Frobenius (left)
pseudo-Frobenius (right)
quasi-duo (left)
quasi-duo (right)
quasi-Frobenius
reversible
self-injective (left)
self-injective (right)
semilocal
semiperfect
semiprimary
semiregular
simple-injective (left)
simple-injective (right)
stable range 1
stably finite
strongly $\pi$-regular
symmetric
T-nilpotent radical (left)
T-nilpotent radical (right)
top regular
Zorn

The ring lacks the following properties:

Baer
Bezout domain (left)
Bezout domain (right)
connected
division ring
domain
free ideal ring (left)
free ideal ring (right)
fully prime
fully semiprime
hereditary (left)
hereditary (right)
local
nonsingular (left)
nonsingular (right)
Ore domain (left)
Ore domain (right)
primary
prime
primitive (left)
primitive (right)
principal ideal domain (left)
principal ideal domain (right)
reduced
Rickart (left)
Rickart (right)
semi free ideal ring
semihereditary (left)
semihereditary (right)
semiprime
semiprimitive
semisimple
simple
simple Artinian
simple socle (left)
simple socle (right)
strongly regular
top simple
top simple Artinian
uniform (left)
uniform (right)
unit regular
V ring (left)
V ring (right)
valuation ring (left)
valuation ring (right)
von Neumann regular

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