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Do you know a field $K$ other than $F_p$ which is the endomorphism ring of an abelian group $G$?

I doubt that there is one because as $G$ gets bigger, $End(G)$ seems to be more and more noncommutative.

This question is inspired by my previous request for examples of rings not arising as endomorphism rings.

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up vote 7 down vote accepted

$\mathbb{Q}$ is the endomorphism ring of $\mathbb{Q}$.

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