Ring $R_{ 187 }$

Non lift/rad matrix ring over a lift/rad base ring

Description:

$M_2(R)$ where $R=R_{186}$

Keywords matrix ring

Reference(s):

  • A. J. Diesl, S. J. Dittmer, and P. P. Nielsen. Idempotent lifting and ring extensions. (2016) @ Theorem 2.1 p 2
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 annihilator
ACC principal
Artinian
Bezout
Bezout domain
cogenerator ring
coherent
cohopfian
continuous
CS
DCC annihilator
distributive
dual
duo
essential socle
FI-injective
finite uniform dimension
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
free ideal ring
Goldie
hereditary
Ikeda-Nakayama
Kasch
linearly compact
max ring
McCoy
Noetherian
nonsingular
nonzero socle
Ore domain
Ore ring
PCI ring
perfect
primitive
principal ideal domain
principal ideal ring
principally injective
pseudo-Frobenius
quasi-continuous
quasi-duo
Rickart
self-injective
semi-Artinian
semi-Noetherian
semihereditary
serial
simple socle
simple-injective
T-nilpotent radical
UGP ring
uniform
uniserial domain
uniserial ring
V ring
Legend
  • = has the property
  • = does not have the property
  • = information not in database

(Nothing was retrieved.)

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