Ring $R_{ 191 }$

Non strongly π-regular matrix ring over a strongly π-regular ring

Description:

$M_2(R_{190})$ using the base ring $R_{190}$

Keywords matrix ring

Reference(s):

  • F. Cedó and L. H. Rowen. Addendum to “Examples of semiperfect rings”. (1998) @ (corrections)
  • L. H. Rowen. Examples of semiperfect rings. (1989) @ Example 2.4 pp 279-280
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
subdirectly irreducible
symmetric
top regular
top simple
top simple Artinian
unit regular
von Neumann regular
weakly clean
Zorn
Asymmetric properties
left Name right
ACC annihilator
ACC principal
Bezout
co-Hopfian
coherent
continuous
CS
DCC annihilator
FI-injective
finitely generated socle
Ikeda-Nakayama
McCoy
nonsingular
Ore ring
principally injective
quasi-continuous
quasi-duo
Rickart
semi-Noetherian
serial
Artinian
Bezout domain
cogenerator ring
distributive
dual
duo
essential socle
finite uniform dimension
finitely cogenerated
finitely pseudo-Frobenius
free ideal ring
Goldie
hereditary
Kasch
linearly compact
max ring
Noetherian
nonzero socle
Ore domain
PCI ring
perfect
primitive
principal ideal domain
principal ideal ring
pseudo-Frobenius
self-injective
semi-Artinian
semihereditary
simple socle
T-nilpotent radical
uniform
uniserial domain
uniserial ring
V ring
simple-injective
UGP ring
Legend
  • = has the property
  • = does not have the property
  • = information not in database

(Nothing was retrieved.)

Name Description
Left socle $\{0\}$
Right socle $\{0\}$