Ring $R_{ 194 }$

Principal ideal domain that is not Nagata

Description:

(to be added)

Reference(s):

  • R. C. Heitmann. A locally Nagata PID that is not Nagata. (2022) @ (main example)
Known Properties
Name
$\pi$-regular
$h$-local domain
$I_0$
algebraically closed field
almost maximal domain
almost maximal ring
almost maximal valuation ring
analytically normal
analytically unramified
Archimedean field
Artinian
Boolean
characteristic 0 field
clean
cogenerator ring
cohopfian
complete discrete valuation ring
continuous
countable
discrete valuation ring
division ring
dual
essential socle
Euclidean domain
Euclidean field
exchange
FGC
FI-injective
field
finite
finitely cogenerated
Frobenius
fully prime
fully semiprime
Goldman domain
Henselian local
Jacobson
Kasch
lift/rad
linearly compact
local
local complete intersection
max ring
maximal ring
maximal valuation ring
N-2
nil radical
nilpotent radical
nonzero socle
ordered field
PCI ring
perfect
perfect field
periodic
potent
primary
primitive
principally injective
pseudo-Frobenius
Pythagorean field
quadratically closed field
quasi-Frobenius
rad-nil
regular local
self-injective
semi-Artinian
semilocal
semiperfect
semiprimary
semiprimitive
semiregular
semisimple
serial
simple
simple Artinian
simple socle
simple-injective
stable range 1
strongly $\pi$-regular
strongly regular
T-nilpotent radical
top regular
top simple
top simple Artinian
UGP ring
uniserial domain
uniserial ring
unit regular
V ring
valuation domain
valuation ring
von Neumann regular
weakly clean
Zorn
?-ring
complete local
excellent
J-2
Nagata
quasi-excellent
torch
universally Japanese
2-primal
Abelian
ACC annihilator
ACC principal
almost Dedekind domain
anti-automorphic
arithmetical
Armendariz
atomic domain
Baer
Bezout
Bezout domain
catenary
Cohen-Macaulay
coherent
commutative
compressible
CS
DCC annihilator
Dedekind domain
Dedekind finite
directly irreducible
distributive
domain
duo
finite uniform dimension
finitely generated socle
finitely pseudo-Frobenius
free ideal ring
GCD domain
Goldie
Gorenstein
Grothendieck
hereditary
IBN
IC ring
Ikeda-Nakayama
involutive
J-0
J-1
Krull domain
McCoy
Mori domain
N-1
NI ring
Noetherian
nonsingular
normal
normal domain
Ore domain
Ore ring
orthogonally finite
polynomial identity
prime
principal ideal domain
principal ideal ring
Prufer domain
quasi-continuous
quasi-duo
reduced
regular
reversible
Rickart
Schreier domain
semi free ideal ring
semi-Noetherian
semicommutative
semihereditary
semiprime
stably finite
strongly connected
symmetric
uniform
unique factorization domain
universally catenary
Legend
  • = has the property
  • = does not have the property
  • = information not in database

(Nothing was retrieved.)

Name Description
Idempotents $\{0,1\}$
Left singular ideal $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Zero divisors $\{0\}$