Description: The groupring $\Bbb Q[G]$ where $G$ is the nonimmersable group described in the paper.

Notes: This is a domain that is not a subring of any division ring.

Keywords group ring

Reference(s):

- A. L. Malcev, On The Immersion Of An Algebraic Ring Into A Field, Mathematische Annalen Vol 113 Issue 1 Pp 686-691, (1937). Section 3

This ring has the following properties:

The ring lacks the following properties:

Artinian (left)
Artinian (right)
Bezout domain (left)
Bezout domain (right)
cogenerator ring (left)
cogenerator ring (right)
cohopfian (left)
cohopfian (right)
commutative
distributive (left)
distributive (right)
division ring
dual (left)
dual (right)
essential socle (left)
essential socle (right)
FI-injective (left)
FI-injective (right)
finite
finite uniform dimension (left)
finite uniform dimension (right)
finitely cogenerated (left)
finitely cogenerated (right)
Frobenius
Goldie (left)
Goldie (right)
Kasch (left)
Kasch (right)
Noetherian (left)
Noetherian (right)
nonzero socle (left)
nonzero socle (right)
Ore domain (left)
Ore domain (right)
perfect (left)
perfect (right)
primary
principal ideal domain (left)
principal ideal domain (right)
principal ideal ring (left)
principal ideal ring (right)
principally injective (left)
principally injective (right)
pseudo-Frobenius (left)
pseudo-Frobenius (right)
quasi-Frobenius
self-injective (left)
self-injective (right)
semiprimary
semisimple
serial (left)
serial (right)
simple Artinian
simple socle (left)
simple socle (right)
strongly $\pi$-regular
strongly regular
uniform (left)
uniform (right)
unit regular
valuation ring (left)
valuation ring (right)
von Neumann regular

We don't know if the ring has or lacks the following properties:

$\pi$-regular
$I_0$
ACC annihilator (left)
ACC annihilator (right)
ACC principal (left)
ACC principal (right)
Bezout (left)
Bezout (right)
clean
coherent (left)
coherent (right)
continuous (left)
continuous (right)
CS (left)
CS (right)
DCC annihilator (left)
DCC annihilator (right)
duo (left)
duo (right)
exchange
finitely generated socle (left)
finitely generated socle (right)
finitely pseudo-Frobenius (left)
finitely pseudo-Frobenius (right)
free ideal ring (left)
free ideal ring (right)
fully prime
fully semiprime
hereditary (left)
hereditary (right)
IBN
Ikeda-Nakayama (left)
Ikeda-Nakayama (right)
lift/rad
local
nil radical
nilpotent radical
Ore ring (left)
Ore ring (right)
polynomial identity
primitive (left)
primitive (right)
quasi-continuous (left)
quasi-continuous (right)
quasi-duo (left)
quasi-duo (right)
semi free ideal ring
semihereditary (left)
semihereditary (right)
semilocal
semiperfect
semiprimitive
semiregular
simple
simple-injective (left)
simple-injective (right)
stable range 1
stably finite
T-nilpotent radical (left)
T-nilpotent radical (right)
top regular
top simple
top simple Artinian
V ring (left)
V ring (right)
weakly clean
Zorn