Ring $R_{ 184 }$

$\mathbb Q[[X]]$

Description:

The power series ring $\mathbb Q[[X]]$ over the rationals

Keywords power series ring

Reference(s):

  • (Citation needed)


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