Ring detail


Name: $F_2[\mathbb Q_8]$

Description: Group ring of the quaternion group $\mathbb Q_8$ with the field of two elements $F_2$.

Notes:

Keywords group 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) connected 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 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 local NI (nilpotents form an ideal) nil radical nilpotent radical Noetherian (left) Noetherian (right) nonzero socle (left) nonzero socle (right) orthogonally finite perfect (left) perfect (right) primary 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 strongly connected T-nilpotent radical (left) T-nilpotent radical (right) top regular top simple top simple Artinian weakly clean Zorn