Ring $R_{ 157 }$

$F_2[S_4]$

Description:

The group ring $F_2[S_4]$ of the symmetric group $S_4$ over the field of two elements $F_2$.

Notes: A non-local, irreducible group ring

Keywords group ring

Reference(s):

  • (Citation needed)
    • Symmetric properties
    Name
    $\pi$-regular
    $I_0$
    2-primal
    Abelian
    anti-automorphic
    Armendariz
    Baer
    Boolean
    clean
    commutative
    compressible
    countable
    Dedekind finite
    directly irreducible
    division ring
    domain
    exchange
    field
    finite
    Frobenius
    fully prime
    fully semiprime
    IBN
    IC ring
    involutive
    lift/rad
    local
    NI ring
    nil radical
    nilpotent radical
    orthogonally finite
    periodic
    polynomial identity
    potent
    primary
    prime
    quasi-Frobenius
    reduced
    reversible
    semi free ideal ring
    semicommutative
    semilocal
    semiperfect
    semiprimary
    semiprime
    semiprimitive
    semiregular
    semisimple
    simple
    simple Artinian
    stable range 1
    stably finite
    strongly $\pi$-regular
    strongly connected
    strongly regular
    symmetric
    top regular
    top simple
    top simple Artinian
    unit regular
    von Neumann regular
    weakly clean
    Zorn
    Asymmetric properties
    left Name right
    ACC annihilator
    ACC principal
    Artinian
    Bezout
    Bezout domain
    cogenerator ring
    coherent
    cohopfian
    continuous
    CS
    DCC annihilator
    distributive
    dual
    duo
    essential socle
    FI-injective
    finite uniform dimension
    finitely cogenerated
    finitely generated socle
    finitely pseudo-Frobenius
    free ideal ring
    Goldie
    hereditary
    Ikeda-Nakayama
    Kasch
    linearly compact
    max ring
    McCoy
    Noetherian
    nonsingular
    nonzero socle
    Ore domain
    Ore ring
    PCI ring
    perfect
    primitive
    principal ideal domain
    principal ideal ring
    principally injective
    pseudo-Frobenius
    quasi-continuous
    quasi-duo
    Rickart
    self-injective
    semi-Artinian
    semi-Noetherian
    semihereditary
    serial
    simple socle
    simple-injective
    T-nilpotent radical
    UGP ring
    uniform
    uniserial domain
    uniserial ring
    V ring
    Legend
    • = has the property
    • = does not have the property
    • = information not in database
    Name Measure
    cardinality 16,777,216
    Krull dimension (classical) 0

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