Ring $R_{ 211 }$

Non-atomic polynomial ring

Description:

The polynomial ring of $R_{210}$ in a single variable.

Keywords polynomial ring

Reference(s):

  • M. Roitman. Polynomial extensions of atomic domains. (1993) @ Example 5.1
Known Properties
Name
$\pi$-regular
$h$-local domain
$I_0$
2-primal
?-ring
Abelian
ACC annihilator
ACC principal
algebraically closed field
almost Dedekind domain
almost maximal domain
almost maximal ring
almost maximal valuation ring
analytically normal
analytically unramified
anti-automorphic
Archimedean field
arithmetical
Armendariz
Artinian
atomic domain
Baer
Bezout
Bezout domain
Boolean
catenary
characteristic 0 field
clean
co-Hopfian
cogenerator ring
Cohen-Macaulay
coherent
commutative
complete discrete valuation ring
complete local
compressible
continuous
countable
CS
DCC annihilator
Dedekind domain
Dedekind finite
directly irreducible
discrete valuation ring
distributive
division ring
domain
dual
duo
essential socle
Euclidean domain
Euclidean field
excellent
exchange
FGC
FI-injective
field
finite
finite uniform dimension
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
free ideal ring
Frobenius
fully prime
fully semiprime
GCD domain
Goldie
Goldman domain
Gorenstein
Grothendieck
Henselian local
hereditary
IBN
IC ring
Ikeda-Nakayama
involutive
J-0
J-1
J-2
Jacobson
Kasch
Krull domain
lift/rad
linearly compact
local
local complete intersection
max ring
maximal ring
maximal valuation ring
McCoy
Mori domain
N-1
N-2
Nagata
NI ring
nil radical
nilpotent radical
Noetherian
nonsingular
nonzero socle
normal
normal domain
ordered field
Ore domain
Ore ring
orthogonally finite
PCI ring
perfect
perfect field
periodic
polynomial identity
potent
primary
prime
primitive
principal ideal domain
principal ideal ring
principally injective
Prufer domain
pseudo-Frobenius
Pythagorean field
quadratically closed field
quasi-continuous
quasi-duo
quasi-excellent
quasi-Frobenius
rad-nil
reduced
regular
regular local
reversible
Rickart
Schreier domain
self-injective
semi free ideal ring
semi-Artinian
semi-Noetherian
semicommutative
semihereditary
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
semisimple
serial
simple
simple Artinian
simple socle
simple-injective
stable range 1
stably finite
strongly $\pi$-regular
strongly connected
strongly regular
subdirectly irreducible
symmetric
T-nilpotent radical
top regular
top simple
top simple Artinian
torch
UGP ring
uniform
unique factorization domain
uniserial domain
uniserial ring
unit regular
universally catenary
universally Japanese
V ring
valuation domain
valuation ring
von Neumann regular
weakly clean
Zorn
Legend
  • = has the property
  • = does not have the property
  • = information not in database

(Nothing was retrieved.)

Name Description
Idempotents $\{0,1\}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$
Zero divisors $\{0\}$