Ring $R_{ 50 }$

$\mathbb R[x,y,z]/(x^2,y^2, xz,yz,z^2-xy)$

Description:

polynomial ring over the real numbers mod the ideal generated by $x^2, y^2, xz,yz,z^2-xy$

Keywords polynomial ring quotient ring

Reference(s):

  • T. Lam. Lectures on modules and rings. (2012) @ Section 15D Example 6 p 419


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