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Is there a ring $R$ for which every ring is isomorphic to the endomorphism ring of some $R$-module (on a fixed side, left or right, so either-or is not allowed)? Here, rings are always required to be unital.

The ring $R=\mathbb{Z}$ does not work. For example, the finite field with $4$ elements is not isomorphic to the endomorphism ring of any abelian group. Also, any example for $R$ that works must have characteristic $0$, or else, only rings whose characteristic divides that of $R$ could be isomorphic to the endomorphism ring of some $R$-module. Finally, no field $R$ would work, because any nonzero commutative ring that is not isomorphic to $R$ itself will not be isomorphic to the endomorphism ring of any $R$-vector space.

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