Ring $R_{ 177 }$

$\prod_{i=0}^\infty \mathbb Q$

Description:

The product ring of countably many copies of $\mathbb Q$

Keywords direct product

Reference(s):

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