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No nilpotent elements

Groups, Rings, Domains, Modules, etc, Galois theory
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Tolaso J Kos
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No nilpotent elements

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Post by Tolaso J Kos » 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 $2$.
Imagination is much more important than knowledge.

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