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
distributive
J-0
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
catenary
clean
co-Hopfian
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
J-1
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
subdirectly irreducible
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 $\{0,1\}$