Ring $R_{ 141 }$

non-$h$-local domain

Description:

Let $G$ be the subgroup of "eventually constant" sequences in $\mathbb Z^\mathbb N$ (meaning except for finitely many positions, the positions are equal). $G$ is a lattice ordered group with the order $(z_n)\leq (z'_n)$ given by $z_i\leq z'_i$ for all $i\in \mathbb N$. The desired ring is the Jaffard-Ohm-Kaplansky construction that yields a Bezout domain with value group $G$.

Keywords Jaffard-Ohm-Kaplansky construction

Reference(s):

  • (Citation needed)


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

    (Nothing was retrieved.)

    Name Description
    Idempotents $\{0,1\}$
    Left singular ideal $\{0\}$
    Left socle $\{0\}$
    Nilpotents $\{0\}$
    Right singular ideal $\{0\}$
    Right socle $\{0\}$
    Zero divisors $\{0\}$