Ring $R_{ 104 }$

$\prod_{i=1}^\infty \mathbb Q[[X,Y]]$

Description:

Countable direct product of the formal power series ring $\mathbb Q[[X,Y]]$ in two indeterminates.

Keywords direct product power series ring

Reference(s):

  • J.-P. Soublin. Anneaux et modules coh{\'e}rents. (1970) @ Proposition 18 p 469


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

(Nothing was retrieved.)

Name Description
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$