No nilpotent elements
Posted: Thu May 19, 2016 10:26 am
Let $\mathcal{R}$ be a ring such that:
$$\text{there exists an $n \geq 2$ such that: $a^n =a$ forall $a \in \mathcal{R}$}$$
Prove that $\mathcal{R}$ has no zero nilpotent elements. Furthemore, if $n$ is even prove that the characteristic of $\mathcal{R}$ is $2$.
$$\text{there exists an $n \geq 2$ such that: $a^n =a$ forall $a \in \mathcal{R}$}$$
Prove that $\mathcal{R}$ has no zero nilpotent elements. Furthemore, if $n$ is even prove that the characteristic of $\mathcal{R}$ is $2$.