Let $R$ be a commutative ring with unity of prime characteristic $p$. If $a\in R$ is nilpotent then does $\exists n \in \mathbb N$ such that $(1+a)^n=1$ ?
2026-03-25 13:34:20.1774445660
Let $R$ be a commutative ring with unity of prime characteristic $p$. If $a\in R$ is nilpotent then is $1+a$ unipotent?
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Yes, because we have
$$(1+a)^{p^e} = 1+a^{p^e} = 1 \text{ for } e \gg 0.$$