Description: Quotient ring of the integers (1) by an ideal $(n)$ where $n$ is a squarefree number.

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)
Baer
Bezout (left)
Bezout (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
distributive (left)
distributive (right)
dual (left)
dual (right)
duo (left)
duo (right)
essential socle (left)
essential socle (right)
exchange
FI-injective (left)
FI-injective (right)
finite
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
fully semiprime
Goldie (left)
Goldie (right)
hereditary (left)
hereditary (right)
I_0
IBN
Kasch (left)
Kasch (right)
lift/rad
nil radical
nilpotent radical
Noetherian (left)
Noetherian (right)
nonsingular (left)
nonsingular (right)
nonzero socle (left)
nonzero socle (right)
Ore ring (left)
Ore ring (right)
orthogonally finite
perfect (left)
perfect (right)
polynomial identity
principal ideal ring (left)
principal ideal ring (right)
principally injective (left)
principally injective (right)
pseudo-Frobenius (left)
pseudo-Frobenius (right)
quasi-duo (left)
quasi-duo (right)
quasi-Frobenius
reduced
reversible
Rickart (left)
Rickart (right)
self-injective (left)
self-injective (right)
semihereditary (left)
semihereditary (right)
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
semisimple
serial (left)
serial (right)
simple-injective (left)
simple-injective (right)
stable range 1
stably finite
strongly $\pi$-regular
strongly regular
symmetric
T-nilpotent radical (left)
T-nilpotent radical (right)
top regular
unit regular
V ring (left)
V ring (right)
von Neumann regular
Zorn

The ring lacks the following properties:

Bezout domain (left)
Bezout domain (right)
connected
division ring
domain
free ideal ring (left)
free ideal ring (right)
fully prime
local
Ore domain (left)
Ore domain (right)
primary
prime
primitive (left)
primitive (right)
principal ideal domain (left)
principal ideal domain (right)
semi free ideal ring
simple
simple Artinian
simple socle (left)
simple socle (right)
top simple
top simple Artinian
uniform (left)
uniform (right)
valuation ring (left)
valuation ring (right)

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