Ring $R_{ 169 }$

Kerr's Goldie ring with non-Goldie matrix ring

Description:

(to be elaborated later)

Notes: $M_2(R)$ does not satisfy ACC annihilator on either side.

Keywords polynomial ring quotient ring

Reference(s):

  • J. W. Kerr. An example of a Goldie ring whose matrix ring is not Goldie. (1979) @ Whole article


Known Properties
Name
$\pi$-regular
$h$-local domain
$I_0$
?-ring
ACC principal
almost Dedekind domain
almost maximal domain
almost maximal ring
almost maximal valuation ring
analytically normal
analytically unramified
arithmetical
Armendariz
atomic domain
Baer
Bezout
Bezout domain
catenary
clean
cogenerator ring
coherent
cohopfian
complete local
continuous
countable
CS
directly irreducible
distributive
domain
essential socle
exchange
FGC
finitely cogenerated
finitely pseudo-Frobenius
GCD domain
Goldman domain
Henselian local
Ikeda-Nakayama
J-0
J-1
J-2
Jacobson
Kasch
Krull domain
lift/rad
linearly compact
local
max ring
maximal ring
maximal valuation ring
Mori domain
N-1
N-2
nil radical
nilpotent radical
nonsingular
nonzero socle
normal
normal domain
Ore domain
perfect
potent
primary
prime
Prufer domain
quasi-continuous
rad-nil
reduced
Rickart
Schreier domain
semi free ideal ring
semi-Artinian
semi-Noetherian
semihereditary
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
serial
simple socle
simple-injective
stable range 1
strongly $\pi$-regular
strongly connected
T-nilpotent radical
top regular
top simple
top simple Artinian
torch
UGP ring
uniform
unique factorization domain
uniserial domain
uniserial ring
universally catenary
universally Japanese
valuation domain
valuation ring
weakly clean
Zorn
algebraically closed field
Archimedean field
Artinian
Boolean
characteristic 0 field
Cohen-Macaulay
complete discrete valuation ring
Dedekind domain
discrete valuation ring
division ring
dual
Euclidean domain
Euclidean field
excellent
FI-injective
field
finite
free ideal ring
Frobenius
fully prime
fully semiprime
Gorenstein
Grothendieck
hereditary
local complete intersection
Nagata
Noetherian
ordered field
PCI ring
perfect field
periodic
primitive
principal ideal domain
principal ideal ring
principally injective
pseudo-Frobenius
Pythagorean field
quadratically closed field
quasi-excellent
quasi-Frobenius
regular
regular local
self-injective
semisimple
simple
simple Artinian
strongly regular
unit regular
V ring
von Neumann regular
2-primal
Abelian
ACC annihilator
anti-automorphic
commutative
compressible
DCC annihilator
Dedekind finite
duo
finite uniform dimension
finitely generated socle
Goldie
IBN
IC ring
involutive
McCoy
NI ring
Ore ring
orthogonally finite
polynomial identity
quasi-duo
reversible
semicommutative
stably finite
symmetric
Legend
  • = has the property
  • = does not have the property
  • = information not in database

(Nothing was retrieved.)

(Nothing was retrieved.)