Ring $R_{ 146 }$

Facchini's torch ring

Description:

See the expanded details page. It is given as an example of a torch ring that is not a split null extension.

Notes: Has characteristic $p^2$.

Keywords ring of Witt vectors

Reference(s):

  • A. Facchini. On the structure of torch rings. (1983) @ Section 1


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

(Nothing was retrieved.)

Name Description
Idempotents $\{0,1\}$