Characteristic three
= Characteristic three
{title2=$\operatorname{char}K=3$}
A <field> has characteristic three when $1+1+1=0$. The binomial identity then becomes $(a+b)^3=a^3+b^3$, and $X^3-1=(X-1)^3$. Thus a <cyclic shift operator> on three coordinates has a repeated-root <minimal polynomial> in this characteristic and cannot be diagonalizable.