Ring $R_{ 117 }$

$\mathbb Q[\mathbb Q]$

Description:

The group ring of the group $(\mathbb Q, +)$ over the field $\mathbb Q$.

Keywords group ring

Reference(s):

  • K. A. Loper. Almost Dedekind domains which are not Dedekind. (2006) @ Theorem 36 (item 2) p 291


Known Properties
Name
$h$-local domain
almost maximal ring
catenary
J-0
J-1
J-2
Jacobson
max ring
N-2
semi-Noetherian
stable range 1
UGP ring
universally catenary
universally Japanese
$\pi$-regular
$I_0$
?-ring
ACC principal
algebraically closed field
almost maximal domain
almost maximal valuation ring
analytically normal
analytically unramified
Archimedean field
Artinian
atomic domain
Boolean
characteristic 0 field
clean
cogenerator ring
Cohen-Macaulay
cohopfian
complete discrete valuation ring
complete local
continuous
Dedekind domain
discrete valuation ring
division ring
dual
essential socle
Euclidean domain
Euclidean field
excellent
exchange
FGC
FI-injective
field
finite
finitely cogenerated
free ideal ring
Frobenius
fully prime
fully semiprime
Goldman domain
Gorenstein
Grothendieck
Henselian local
hereditary
Kasch
Krull domain
linearly compact
local
local complete intersection
maximal ring
maximal valuation ring
Mori domain
Nagata
Noetherian
nonzero socle
ordered field
PCI ring
perfect
perfect field
periodic
potent
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
semilocal
semiperfect
semiprimary
semiregular
semisimple
serial
simple
simple Artinian
simple socle
strongly $\pi$-regular
strongly regular
top regular
top simple
top simple Artinian
torch
unique factorization domain
uniserial domain
uniserial ring
unit regular
V ring
valuation domain
valuation ring
von Neumann regular
weakly clean
Zorn
2-primal
Abelian
ACC annihilator
almost Dedekind domain
anti-automorphic
arithmetical
Armendariz
Baer
Bezout
Bezout domain
coherent
commutative
compressible
countable
CS
DCC annihilator
Dedekind finite
directly irreducible
distributive
domain
duo
finite uniform dimension
finitely generated socle
finitely pseudo-Frobenius
GCD domain
Goldie
IBN
IC ring
Ikeda-Nakayama
involutive
lift/rad
McCoy
N-1
NI ring
nil radical
nilpotent radical
nonsingular
normal
normal domain
Ore domain
Ore ring
orthogonally finite
polynomial identity
prime
Prufer domain
quasi-continuous
quasi-duo
rad-nil
reduced
reversible
Rickart
Schreier domain
semi free ideal ring
semicommutative
semihereditary
semiprime
semiprimitive
simple-injective
stably finite
strongly connected
symmetric
T-nilpotent radical
uniform
Legend
  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
cardinality $\aleph_0$
Krull dimension (classical) 1
Name Description
Idempotents $\{0,1\}$
Jacobson radical $\{0\}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$
Zero divisors $\{0\}$