Ring detail


Name: $\mathbb Z/(n)$, $n$ squarefree

Description: Quotient ring of the integers (1) by an ideal $(n)$ where $n$ is a squarefree number.

Notes:

Keywords quotient ring

Reference(s):

  • (Citation needed)


  • This ring has the following properties:
    $\pi$-regular 2-primal Abelian ACC annihilator (left) ACC annihilator (right) ACC principal (left) ACC principal (right) Artinian (left) Artinian (right) Baer Bezout (left) Bezout (right) clean cogenerator ring (left) cogenerator ring (right) coherent (left) coherent (right) cohopfian (left) cohopfian (right) commutative continuous (left) continuous (right) DCC annihilator (left) DCC annihilator (right) Dedekind finite distributive (left) distributive (right) dual (left) dual (right) duo (left) duo (right) essential socle (left) essential socle (right) exchange FI-injective (left) FI-injective (right) finite 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) Frobenius fully semiprime Goldie (left) Goldie (right) hereditary (left) hereditary (right) I_0 IBN Kasch (left) Kasch (right) lift/rad nil radical nilpotent radical Noetherian (left) Noetherian (right) nonsingular (left) nonsingular (right) nonzero socle (left) nonzero socle (right) Ore ring (left) Ore ring (right) orthogonally finite perfect (left) perfect (right) polynomial identity principal ideal ring (left) principal ideal ring (right) principally injective (left) principally injective (right) pseudo-Frobenius (left) pseudo-Frobenius (right) quasi-duo (left) quasi-duo (right) quasi-Frobenius reduced reversible Rickart (left) Rickart (right) self-injective (left) self-injective (right) semihereditary (left) semihereditary (right) semilocal semiperfect semiprimary semiprime semiprimitive semiregular semisimple serial (left) serial (right) simple-injective (left) simple-injective (right) stable range 1 stably finite strongly $\pi$-regular strongly regular symmetric T-nilpotent radical (left) T-nilpotent radical (right) top regular unit regular V ring (left) V ring (right) von Neumann regular Zorn
    We don't know if the ring has or lacks the following properties: