Ring detail


Name: Local Cohen-Macaulay domain which isn't regular

Description: $k[x,y]_{(x,y)}/(x^2-y^3)$

Krull dimension: 1

Keywords localization polynomial ring quotient ring

Reference(s):

  • (Citation needed)


  • Known Properties
    Name
    $I_0$
    $\pi$-regular
    2-primal
    ACC annihilator
    ACC principal
    Abelian
    Archimedean field
    Artinian
    Baer
    Bezout
    Bezout domain
    CS
    Cohen-Macaulay
    DCC annihilator
    Dedekind domain
    Dedekind finite
    Euclidean domain
    Euclidean field
    FI-injective
    Frobenius
    GCD domain
    Goldie
    Gorenstein
    Grothendieck
    IBN
    Ikeda-Nakayama
    J-0
    J-1
    J-2
    Jacobson (Hilbert)
    Japanese (N-2)
    Kasch
    Krull domain
    Mori domain
    N-1
    NI (nilpotents form an ideal)
    Nagata
    Noetherian
    Ore domain
    Ore ring
    Prufer domain
    Pythagorean field
    Rickart
    Schreier domain
    T-nilpotent radical
    V ring
    Zorn
    algebraically closed field
    analytically normal
    analytically unramified
    atomic domain
    catenary
    characteristic 0 field
    clean
    cogenerator ring
    coherent
    cohopfian
    commutative
    complete local
    compressible
    connected
    continuous
    distributive
    division ring
    domain
    dual
    duo
    essential socle
    excellent
    exchange
    field
    finite
    finite uniform dimension
    finitely cogenerated
    finitely generated socle
    finitely pseudo-Frobenius
    free ideal ring
    fully prime
    fully semiprime
    hereditary
    lift/rad
    local
    local complete intersection
    nil radical
    nilpotent radical
    nonsingular
    nonzero socle
    normal
    normal domain
    ordered field
    orthogonally finite
    perfect
    perfect field
    polynomial identity
    primary
    prime
    primitive
    principal ideal domain
    principal ideal ring
    principally injective
    pseudo-Frobenius
    quadratically closed field
    quasi-Frobenius
    quasi-continuous
    quasi-duo
    quasi-excellent
    rad-nil
    reduced
    regular
    regular local
    reversible
    self-injective
    semi free ideal ring
    semicommutative (SI condition, zero-insertive)
    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
    symmetric
    top regular
    top simple
    top simple Artinian
    uniform
    unique factorization domain
    unit regular
    universally Japanese
    universally catenary
    valuation ring
    von Neumann regular
    weakly clean