Ring $R_{ 138 }$

Nagata ring that not quasi-excellent

Description:

See Nishimura, Jun-Ichi. "A few examples of local rings, I." Kyoto Journal of Mathematics 52.1 (2012): 51-87. page 64

Reference(s):

  • C. Rotthaus. Nicht ausgezeichnete, universell japanische Ringe. (1977) @ (somewhere)
  • J. Nishimura. A few examples of local rings, I. (2012) @ Example 2.5
Known Properties
Name
almost maximal domain
almost maximal ring
analytically unramified
countable
finitely pseudo-Frobenius
GCD domain
Goldman domain
Gorenstein
Grothendieck
Henselian local
J-0
J-1
J-2
Krull domain
local complete intersection
Mori domain
regular
regular local
Schreier domain
unique factorization domain
$\pi$-regular
?-ring
algebraically closed field
almost Dedekind domain
almost maximal valuation ring
analytically normal
Archimedean field
arithmetical
Artinian
Bezout
Bezout domain
Boolean
characteristic 0 field
co-Hopfian
cogenerator ring
complete discrete valuation ring
complete local
continuous
Dedekind domain
discrete valuation ring
distributive
division ring
dual
essential socle
Euclidean domain
Euclidean field
excellent
FGC
FI-injective
field
finite
finitely cogenerated
free ideal ring
Frobenius
fully prime
fully semiprime
hereditary
Jacobson
Kasch
linearly compact
max ring
maximal ring
maximal valuation ring
nil radical
nilpotent radical
nonzero socle
ordered field
PCI ring
perfect
perfect field
periodic
primary
primitive
principal ideal domain
principal ideal ring
principally injective
Prufer domain
pseudo-Frobenius
Pythagorean field
quadratically closed field
quasi-excellent
quasi-Frobenius
rad-nil
self-injective
semi free ideal ring
semi-Artinian
semihereditary
semiprimary
semiprimitive
semisimple
serial
simple
simple Artinian
simple socle
strongly $\pi$-regular
strongly regular
subdirectly irreducible
T-nilpotent radical
torch
uniserial domain
uniserial ring
unit regular
V ring
valuation domain
valuation ring
von Neumann regular
Zorn
$h$-local domain
$I_0$
2-primal
Abelian
ACC annihilator
ACC principal
anti-automorphic
Armendariz
atomic domain
Baer
catenary
clean
Cohen-Macaulay
coherent
commutative
compressible
CS
DCC annihilator
Dedekind finite
directly irreducible
domain
duo
exchange
finite uniform dimension
finitely generated socle
Goldie
IBN
IC ring
Ikeda-Nakayama
involutive
lift/rad
local
McCoy
N-1
N-2
Nagata
NI ring
Noetherian
nonsingular
normal
normal domain
Ore domain
Ore ring
orthogonally finite
polynomial identity
potent
prime
quasi-continuous
quasi-duo
reduced
reversible
Rickart
semi-Noetherian
semicommutative
semilocal
semiperfect
semiprime
semiregular
simple-injective
stable range 1
stably finite
strongly connected
symmetric
top regular
top simple
top simple Artinian
UGP ring
uniform
universally catenary
universally Japanese
weakly clean
Legend
  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
Krull dimension (classical) 2
Name Description
Idempotents $\{0,1\}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$
Zero divisors $\{0\}$