Ring detail


Name: local right-not-left Kasch ring

Description: Let $k$ be a field. Let $S$ be the power series ring over $k$ in two noncommuting variables $x,y$. The ring is $R=S/(y^2,yx)$

Notes:

Keywords quotient ring power series ring

Reference(s):

  • (Citation needed)


  • We don't know if the ring has or lacks the following properties:
    $\pi$-regular 2-primal ACC annihilator (left) ACC annihilator (right) ACC principal (left) ACC principal (right) Baer Bezout (left) Bezout (right) coherent (left) coherent (right) cohopfian (left) cohopfian (right) continuous (left) continuous (right) CS (left) CS (right) DCC annihilator (left) DCC annihilator (right) distributive (left) distributive (right) dual (right) duo (left) duo (right) essential socle (left) essential socle (right) FI-injective (left) FI-injective (right) finite uniform dimension (left) finite uniform dimension (right) finitely cogenerated (left) finitely cogenerated (right) finitely generated socle (left) finitely generated socle (right) finitely pseudo-Frobenius (left) finitely pseudo-Frobenius (right) fully semiprime Goldie (left) Goldie (right) hereditary (left) hereditary (right) Ikeda-Nakayama (left) Ikeda-Nakayama (right) NI (nilpotents form an ideal) nil radical Noetherian (left) Noetherian (right) nonsingular (left) nonsingular (right) nonzero socle (left) Ore ring (left) Ore ring (right) perfect (left) perfect (right) polynomial identity principal ideal ring (left) principal ideal ring (right) principally injective (left) principally injective (right) quasi-continuous (left) quasi-continuous (right) reduced reversible Rickart (left) Rickart (right) self-injective (left) semicommutative (SI condition, zero-insertive) semihereditary (left) semihereditary (right) semiprime serial (left) serial (right) simple socle (left) simple socle (right) simple-injective (left) simple-injective (right) strongly $\pi$-regular symmetric T-nilpotent radical (left) T-nilpotent radical (right) uniform (left) uniform (right) valuation ring (left) valuation ring (right) Zorn