|
2 | deleted 19 characters in body | ||
|
Suppose that $A$ is an infinite definable subset of a real closed field $R$ which is a zero-divisor-free ring under operations whose graphs are definable in $R$. Then $A$ is definably isomorphic to one of $R$, $R(\sqrt{-1})$ or the ring of quaternions over $R$. This is a special case of the main result of: Otero, Peterzil, and Pillay, On groups and rings definable in o-minimal expansions of real closed fields. (English summary) , Bull. London Math. Soc. 28 (1996), no. 1, 7–14. |
||||
|
|
1 |
|
||
|
Suppose that $A$ is an infinite definable subset of a real closed field $R$ which is a zero-divisor-free ring under operations whose graphs are definable in $R$. Then $A$ is definably isomorphic to one of $R$, $R(\sqrt{-1})$ or the ring of quaternions over $R$. This is a special case of the main result of: Otero, Peterzil, and Pillay, On groups and rings definable in o-minimal expansions of real closed fields. (English summary) Bull. London Math. Soc. 28 (1996), no. 1, 7–14. |
||||
