Ring $R_{ 24 }$

Description:

Let $F$ be the field of two elements, $S=F\langle x,y,z\rangle$ and $R=S /I$ where $I=(SxS)^2+(SyS)^2+(SzS)^2 + SxyzS + SyzxS + SzxyS$

Notes: $13$ dimensional $F$ algebra.

Keywords quotient ring