Ring $R_{ 219 }$

$F_2(x)$

Description:

Field of rational polynomials over the field of two elements

Notes: Unlike the case for other prime characteristics, this one is a Pythagorean field

Reference(s):

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

    (Nothing was retrieved.)

    (Nothing was retrieved.)