Ring $R_{ 156 }$

Description:

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