Ring $R_{ 156 }$

Division algebra with no anti-automorphism


Let $K$ be the unique cubic subextension of $\mathbb Q(\zeta_7)$. Let $\sigma$ be a generator of the Galois group (of order $3$) for $K/\mathbb Q$. Define the ring $R$ by adjoining an indeterminate $x$ to $K$ with the relations: $xkx^{-1}=\sigma k$ for all $k\in K$ and $x^3=2$. This is a central simple $\mathbb Q$ algebra with Brauer group of order $3$.

Notes: Central simple $\mathbb Q$ division algebra.

Keywords cyclic algebra


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  • Legend
    • = has the property
    • = does not have the property
    • = information not in database
    Name Measure
    global dimension left: 0right: 0
    Krull dimension (classical) 0
    weak global dimension 0
    Name Description
    Idempotents $\{0,1\}$
    Jacobson radical $\{0\}$
    Left singular ideal $\{0\}$
    Left socle $R$
    Nilpotents $\{0\}$
    Right singular ideal $\{0\}$
    Right socle $R$
    Units $R\setminus\{0\}$
    Zero divisors $\{0\}$