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Apart from $\mathbb{N}$ and $\mathbb{C}$, which other domains satisfy $\forall x, y \in D, x^y \in D$ ,i.e. are closed under exponentiation?

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    What do you mean by $x^y$ in an arbitrary domain? ($x^y$ is not even completely defined over the complex numbers.) Also, you seem to be using the word "domain" in a nonstandard way; the definition I know is that a domain is a ring with no zero divisors, and in particular it needs to be closed under subtraction, which $\mathbb{N}$ isn't.2012-01-07
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    @QiaochuYuan My knowledge of set theory is quite minimal, so I tend to inappropriately generalize terminology. Would 'set' have been more appropriate here?2012-01-07

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