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
anti-automorphic
compressible
fully prime
fully semiprime
involutive
NI ring
orthogonally finite
polynomial identity
subdirectly irreducible
top simple
top simple Artinian
2-primal
Abelian
Armendariz
Baer
Boolean
commutative
division ring
domain
field
finite
Frobenius
local
nilpotent radical
periodic
primary
quasi-Frobenius
reduced
reversible
semi free ideal ring
semicommutative
semiprimary
semiprimitive
semisimple
simple
simple Artinian
strongly $\pi$-regular
strongly connected
strongly regular
symmetric
unit regular
von Neumann regular
$I_0$
clean
countable
Dedekind finite
directly irreducible
exchange
IBN
IC ring
lift/rad
nil radical
potent
prime
semilocal
semiperfect
semiprime
semiregular
stable range 1
stably finite
top 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 $\{0\}$