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
$h$-local domain
$I_0$
almost Dedekind domain
almost maximal domain
almost maximal ring
almost maximal valuation ring
analytically normal
analytically unramified
arithmetical
Bezout
Bezout domain
catenary
clean
coherent
complete local
countable
distributive
exchange
FGC
finitely pseudo-Frobenius
GCD domain
Goldman domain
Henselian local
J-0
J-1
J-2
Jacobson
lift/rad
linearly compact
local
max ring
maximal ring
maximal valuation ring
N-1
N-2
nil radical
nilpotent radical
normal
normal domain
potent
Prufer domain
rad-nil
Schreier domain
semi free ideal ring
semi-Noetherian
semihereditary
semilocal
semiperfect
semiprimitive
semiregular
serial
stable range 1
T-nilpotent radical
top regular
top simple
top simple Artinian
uniserial domain
uniserial ring
universally catenary
universally Japanese
valuation domain
valuation ring
weakly clean
Zorn
$\pi$-regular
?-ring
ACC principal
algebraically closed field
Archimedean field
Artinian
atomic domain
Boolean
characteristic 0 field
co-Hopfian
cogenerator ring
Cohen-Macaulay
complete discrete valuation ring
continuous
Dedekind domain
discrete valuation ring
division ring
dual
essential socle
Euclidean domain
Euclidean field
excellent
FI-injective
field
finite
finitely cogenerated
free ideal ring
Frobenius
fully prime
fully semiprime
Gorenstein
Grothendieck
hereditary
Kasch
Krull domain
local complete intersection
Mori domain
Nagata
Noetherian
nonzero socle
ordered field
PCI ring
perfect
perfect field
periodic
primary
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
semi-Artinian
semiprimary
semisimple
simple
simple Artinian
simple socle
strongly $\pi$-regular
strongly regular
subdirectly irreducible
torch
unique factorization domain
unit regular
V ring
von Neumann regular
2-primal
Abelian
ACC annihilator
anti-automorphic
Armendariz
Baer
commutative
compressible
CS
DCC annihilator
Dedekind finite
directly irreducible
domain
duo
finite uniform dimension
finitely generated socle
Goldie
IBN
IC ring
Ikeda-Nakayama
involutive
McCoy
NI ring
nonsingular
Ore domain
Ore ring
orthogonally finite
polynomial identity
prime
quasi-continuous
quasi-duo
reduced
reversible
Rickart
semicommutative
semiprime
simple-injective
stably finite
strongly connected
symmetric
UGP ring
uniform
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 $\{0\}$