Ring $R_{ 164 }$

$\mathbb Z[X]/(X^2,4X, 8)$

Description:

$R=\mathbb Z[X]/(X^2,4X, 8)$

Keywords polynomial ring quotient ring

Reference(s):

  • (Citation needed)
    • Known Properties
    Name
    analytically unramified
    arithmetical
    Armendariz
    distributive
    J-0
    principally injective
    $h$-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
    cogenerator ring
    complete discrete valuation ring
    continuous
    CS
    Dedekind domain
    discrete valuation ring
    division ring
    domain
    dual
    Euclidean domain
    Euclidean field
    FGC
    FI-injective
    field
    finitely pseudo-Frobenius
    free ideal ring
    Frobenius
    fully prime
    fully semiprime
    GCD domain
    Goldman domain
    Gorenstein
    hereditary
    Ikeda-Nakayama
    Krull domain
    local complete intersection
    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
    pseudo-Frobenius
    Pythagorean field
    quadratically closed field
    quasi-continuous
    quasi-Frobenius
    reduced
    regular
    regular local
    Rickart
    Schreier domain
    self-injective
    semi free ideal ring
    semihereditary
    semiprime
    semiprimitive
    semisimple
    serial
    simple
    simple Artinian
    simple socle
    simple-injective
    strongly regular
    torch
    uniform
    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
    Cohen-Macaulay
    coherent
    cohopfian
    commutative
    complete local
    compressible
    countable
    DCC annihilator
    Dedekind finite
    directly irreducible
    duo
    essential socle
    excellent
    exchange
    finite
    finite uniform dimension
    finitely cogenerated
    finitely generated socle
    Goldie
    Grothendieck
    Henselian local
    IBN
    IC ring
    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
    quasi-duo
    quasi-excellent
    rad-nil
    reversible
    semi-Artinian
    semi-Noetherian
    semicommutative
    semilocal
    semiperfect
    semiprimary
    semiregular
    stable range 1
    stably finite
    strongly $\pi$-regular
    strongly connected
    symmetric
    T-nilpotent radical
    top regular
    top simple
    top simple Artinian
    UGP ring
    universally catenary
    universally Japanese
    weakly clean
    Zorn
    Legend
    • = has the property
    • = does not have the property
    • = information not in database
    Name Measure
    cardinality 32
    Krull dimension (classical) 0
    Name Description
    Idempotents $\{0,1\}$