Could someone explain to me the following sentence?
"A primitive element in a field of order $r$ is a primitive $(r-1)$st root of unity."
Does this mean that for each element $x$ of a field of order $r$ it stands that $x^r-1=0$ and $x^n-1 \neq 0$ for $n<r$ ?
It means that if $F$ is a field of order $r$ (that is, a field having exactly $r$ elements), and $x$ is a primitive element of $F$ (that is, every element of $F$ can be written as a power of $x$), then $x$ is a primitive $r-1$-st root of unity (that is, we have $x^{r-1} = 1$ but $x^n \neq 1$ for every $1 \leq n < r-1$).