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## No nilpotent elements

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

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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