Ring $R_{ 31 }$

Bergman's primitive finite uniform dimension ring

Description:

See the expanded details page.

Expanded details page.

Keywords semigroup ring

Reference(s):

  • A. W. Chatters and C. R. Hajarnavis. Rings with chain conditions. (1980) @ Bergman's example, pp 27-30
Symmetric properties
Name
$\pi$-regular
$I_0$
2-primal
Abelian
anti-automorphic
Armendariz
Baer
Boolean
clean
commutative
compressible
countable
Dedekind finite
directly irreducible
division ring
domain
exchange
field
finite
Frobenius
fully prime
fully semiprime
IBN
IC ring
involutive
lift/rad
local
NI ring
nil radical
nilpotent radical
orthogonally finite
periodic
polynomial identity
potent
primary
prime
quasi-Frobenius
reduced
reversible
semi free ideal ring
semicommutative
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
semisimple
simple
simple Artinian
stable range 1
stably finite
strongly $\pi$-regular
strongly connected
strongly regular
symmetric
top regular
top simple
top simple Artinian
unit regular
von Neumann regular
weakly clean
Zorn
Asymmetric properties
left Name right
ACC principal
Bezout
cogenerator ring
coherent
cohopfian
CS
distributive
dual
FI-injective
finitely pseudo-Frobenius
Ikeda-Nakayama
Kasch
max ring
McCoy
nonzero socle
Ore ring
principally injective
quasi-continuous
quasi-duo
semi-Noetherian
simple socle
simple-injective
UGP ring
uniform
V ring
ACC annihilator
Artinian
Bezout domain
continuous
DCC annihilator
duo
essential socle
finitely cogenerated
free ideal ring
Goldie
hereditary
linearly compact
Noetherian
nonsingular
Ore domain
PCI ring
perfect
principal ideal domain
principal ideal ring
pseudo-Frobenius
Rickart
self-injective
semi-Artinian
semihereditary
serial
uniserial domain
uniserial ring
finite uniform dimension
finitely generated socle
primitive
T-nilpotent radical
Legend
  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
composition length left: $\infty$right: $\infty$
Name Description
Jacobson radical $\{0\}$