It is known that we can define elliptic curves over commutative rings. However can we define an elliptic curve over a noncommutative ring?
This question is considered to some extent in this thesis (Section 4.4) but reaches no conclusion on the matter.
NOTE: By an elliptic curve over a noncommutative ring I do not mean a noncommutative torus.
I asked a similar question on mathoverflow before but got no replies in the affirmative or the negative.