Ring $R_{ 201 }$

Non-IC polynomial ring over an IC ring

Description:

The ring is $S[Y]$ where $S=$$R_{199}$

Keywords matrix ring polynomial ring

Reference(s):

  • D. Khurana and T. Lam. Rings with internal cancellation. (2005) @ Proposition 5.10 p 215
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
Bezout
cogenerator ring
cohopfian
CS
essential socle
finitely cogenerated
finitely pseudo-Frobenius
hereditary
Ikeda-Nakayama
Kasch
max ring
McCoy
nonzero socle
Ore ring
PCI ring
primitive
principal ideal ring
quasi-continuous
quasi-duo
Rickart
semihereditary
simple socle
simple-injective
T-nilpotent radical
V ring
Artinian
Bezout domain
continuous
distributive
dual
duo
FI-injective
free ideal ring
linearly compact
Ore domain
perfect
principal ideal domain
principally injective
pseudo-Frobenius
self-injective
semi-Artinian
serial
UGP ring
uniform
uniserial domain
uniserial ring
ACC annihilator
ACC principal
coherent
DCC annihilator
finite uniform dimension
finitely generated socle
Goldie
Noetherian
nonsingular
semi-Noetherian
Legend
  • = has the property
  • = does not have the property
  • = information not in database

(Nothing was retrieved.)

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