Ring detail


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

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

Notes: Krull dimension $1$.

Keywords quotient ring localization polynomial ring

Reference(s):

  • (Citation needed)


  • The ring lacks the following properties:
    We don't know if the ring has or lacks the following properties:
    $\pi$-regular ACC principal (left) ACC principal (right) Artinian (left) Artinian (right) Bezout (left) Bezout (right) Bezout domain (left) Bezout domain (right) cogenerator ring (left) cogenerator ring (right) coherent (left) coherent (right) cohopfian (left) cohopfian (right) continuous (left) continuous (right) distributive (left) distributive (right) division ring dual (left) dual (right) essential socle (left) essential socle (right) FI-injective (left) FI-injective (right) finite finitely cogenerated (left) finitely cogenerated (right) finitely pseudo-Frobenius (left) finitely pseudo-Frobenius (right) free ideal ring (left) free ideal ring (right) Frobenius fully prime fully semiprime hereditary (left) hereditary (right) Ikeda-Nakayama (left) Ikeda-Nakayama (right) Kasch (left) Kasch (right) nil radical nilpotent radical Noetherian (left) Noetherian (right) nonzero socle (left) nonzero socle (right) perfect (left) perfect (right) primary primitive (left) primitive (right) principal ideal domain (left) principal ideal domain (right) principal ideal ring (left) principal ideal ring (right) principally injective (left) principally injective (right) pseudo-Frobenius (left) pseudo-Frobenius (right) quasi-Frobenius self-injective (left) self-injective (right) semi free ideal ring semihereditary (left) semihereditary (right) semiprimary semiprimitive semisimple serial (left) serial (right) simple simple Artinian simple socle (left) simple socle (right) simple-injective (left) simple-injective (right) strongly $\pi$-regular strongly regular T-nilpotent radical (left) T-nilpotent radical (right) unit regular V ring (left) V ring (right) valuation ring (left) valuation ring (right) von Neumann regular Zorn