[FOM] "Diophantine Complete" rings

[Martin Davis]

Harvey Friedman has proposed the study of Diophantine Complete (DC) rings, 
that is rings with the property that whenever a polynomial with integer 
coefficients has a zero in the ring, it also has an zero in the integers.

I note that any ring which can be homomorphically mapped into the integers 
is obviously DC.
Question: Are there any others?

Obvious examples of rings for which such homomorphisms exist are the rings 
of polynomials in some set of indeterminates. Are there any others?

Martin