Ring $R_{ 132 }$

Samuel's UFD having a non-UFD power series ring

Description:

Let $F$ be a perfect field of characteristic $2$. The ring $R$ is the ring $\mathbb F[x,y,z]/(x^2+y^3+z^7)$ localized at $(x,y,z)$.

Keywords localization polynomial ring quotient ring

Reference(s):

  • P. Samuel. On unique factorization domains. (1961) @ Theorem 4.1 p 9


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

(Nothing was retrieved.)

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