[FOM] "Diophantine Complete" rings

Martin Davis martin at eipye.com
Sun Jul 6 03:14:00 EDT 2003

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?


More information about the FOM mailing list