Ring $R_{ 71 }$

Quasi-continuous ring that is not Ikeda-Nakayama

Description:

Quotient of $\mathbb F_2[x_1, x_2, x_3\ldots ]$ such that $x_i^3=0$ for all $i$, $x_ix_j=0$ for $i\neq j$, and $x_i^2=m\neq 0$ for all $i$. $F_2$ denotes the field of two elements.

Keywords quotient ring

Reference(s):

  • V. Camillo, W. Nicholson, and M. Yousif. Ikeda--Nakayama rings. (2000) @ pp 1000-1010


Known Properties
Name
almost maximal ring
analytically unramified
arithmetical
Armendariz
catenary
distributive
J-0
J-1
J-2
linearly compact
maximal ring
universally catenary
universally Japanese
$h$-local domain
?-ring
ACC annihilator
algebraically closed field
almost Dedekind domain
almost maximal domain
almost maximal valuation ring
analytically normal
Archimedean field
Artinian
atomic domain
Baer
Bezout
Bezout domain
Boolean
characteristic 0 field
cogenerator ring
Cohen-Macaulay
coherent
complete discrete valuation ring
DCC annihilator
Dedekind domain
discrete valuation ring
division ring
domain
dual
Euclidean domain
Euclidean field
excellent
FGC
FI-injective
field
finite
finitely pseudo-Frobenius
free ideal ring
Frobenius
fully prime
fully semiprime
GCD domain
Goldie
Goldman domain
Gorenstein
Grothendieck
hereditary
Ikeda-Nakayama
Krull domain
local complete intersection
maximal valuation ring
Mori domain
N-1
N-2
Nagata
Noetherian
nonsingular
normal
normal domain
ordered field
Ore domain
PCI ring
perfect field
periodic
prime
primitive
principal ideal domain
principal ideal ring
Prufer domain
pseudo-Frobenius
Pythagorean field
quadratically closed field
quasi-excellent
quasi-Frobenius
reduced
regular
regular local
Rickart
Schreier domain
self-injective
semi free ideal ring
semihereditary
semiprime
semiprimitive
semisimple
serial
simple
simple Artinian
simple-injective
strongly regular
torch
unique factorization domain
uniserial domain
uniserial ring
unit regular
V ring
valuation domain
valuation ring
von Neumann regular
$\pi$-regular
$I_0$
2-primal
Abelian
ACC principal
anti-automorphic
clean
cohopfian
commutative
complete local
compressible
continuous
countable
CS
Dedekind finite
directly irreducible
duo
essential socle
exchange
finite uniform dimension
finitely cogenerated
finitely generated socle
Henselian local
IBN
IC ring
involutive
Jacobson
Kasch
lift/rad
local
max ring
McCoy
NI ring
nil radical
nilpotent radical
nonzero socle
Ore ring
orthogonally finite
perfect
polynomial identity
potent
primary
principally injective
quasi-continuous
quasi-duo
rad-nil
reversible
semi-Artinian
semi-Noetherian
semicommutative
semilocal
semiperfect
semiprimary
semiregular
simple socle
stable range 1
stably finite
strongly $\pi$-regular
strongly connected
symmetric
T-nilpotent radical
top regular
top simple
top simple Artinian
UGP ring
uniform
weakly clean
Zorn
Legend
  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
cardinality $\aleph_0$
composition length left: $\infty$right: $\infty$
Krull dimension (classical) 0
Name Description
Idempotents $\{0,1\}$