Ring detail


Name: $\mathbb Z/(n)$, $n$ divisible by two primes and a square

Description: The quotient of the integers by an ideal $(n)$ where $n>1$ is divisible by at least two different primes, and $n$ isn't squarefree

Notes:

Keywords quotient ring

Reference(s):

  • (Citation needed)


  • This ring has the following properties:
    $\pi$-regular $I_0$ 2-primal Abelian ACC annihilator (left) ACC annihilator (right) ACC principal (left) ACC principal (right) Artinian (left) Artinian (right) clean cogenerator ring (left) cogenerator ring (right) coherent (left) coherent (right) cohopfian (left) cohopfian (right) commutative continuous (left) continuous (right) CS (left) CS (right) DCC annihilator (left) DCC annihilator (right) Dedekind finite dual (left) dual (right) duo (left) duo (right) essential socle (left) essential socle (right) exchange 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) Frobenius Goldie (left) Goldie (right) IBN Ikeda-Nakayama (left) Ikeda-Nakayama (right) Kasch (left) Kasch (right) lift/rad NI (nilpotents form an ideal) nil radical nilpotent radical Noetherian (left) Noetherian (right) nonzero socle (left) nonzero socle (right) Ore ring (left) Ore ring (right) orthogonally finite perfect (left) perfect (right) polynomial identity principally injective (left) principally injective (right) pseudo-Frobenius (left) pseudo-Frobenius (right) quasi-continuous (left) quasi-continuous (right) quasi-duo (left) quasi-duo (right) quasi-Frobenius reversible self-injective (left) self-injective (right) semicommutative (SI condition, zero-insertive) semilocal semiperfect semiprimary semiregular simple-injective (left) simple-injective (right) stable range 1 stably finite strongly $\pi$-regular symmetric T-nilpotent radical (left) T-nilpotent radical (right) top regular weakly clean Zorn