Ring $R_{ 145 }$

Trivial extension torch ring

Description:

Let $S$ be ring 144, and Q be its field of fractions, and let $M$ be a maximal ideal of $S$. The ring is the trivial extension $T(S, Q/S_{M})$

Reference(s):

  • T. S. Shores and R. Wiegand. Rings whose finitely generated modules are direct sums of cyclics. (1974) @ Example 4.5 p 166
Known Properties
Name
ACC annihilator
almost maximal ring
catenary
coherent
cohopfian
CS
DCC annihilator
essential socle
FI-injective
finite uniform dimension
finitely cogenerated
finitely generated socle
Goldie
Ikeda-Nakayama
J-0
J-1
J-2
Kasch
nonzero socle
principally injective
quasi-continuous
semi-Noetherian
simple socle
simple-injective
uniform
universally catenary
universally Japanese
$\pi$-regular
$h$-local domain
$I_0$
ACC principal
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
Cohen-Macaulay
complete discrete valuation ring
complete local
continuous
countable
Dedekind domain
discrete valuation ring
division ring
domain
dual
Euclidean domain
Euclidean field
excellent
exchange
field
finite
free ideal ring
Frobenius
fully prime
fully semiprime
GCD domain
Goldman domain
Gorenstein
Grothendieck
Henselian local
hereditary
Jacobson
Krull domain
lift/rad
linearly compact
local
local complete intersection
max ring
maximal ring
maximal valuation ring
Mori domain
N-1
N-2
Nagata
nil radical
nilpotent radical
Noetherian
nonsingular
normal
normal domain
ordered field
Ore domain
PCI ring
perfect
perfect field
periodic
potent
primary
prime
primitive
principal ideal domain
principal ideal ring
Prufer domain
pseudo-Frobenius
Pythagorean field
quadratically closed field
quasi-excellent
quasi-Frobenius
rad-nil
reduced
regular
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
T-nilpotent radical
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
semilocal
stable range 1
stably finite
strongly connected
symmetric
top regular
torch
UGP ring
Legend
  • = has the property
  • = does not have the property
  • = information not in database

(Nothing was retrieved.)

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