“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 16203 |
|
| Abstract: | |
|
We study discrete orderings in the real spectrum of a commutative ring by defining discrete prime cones and give an algebro-geometric meaning to some kind of diophantine problems over discretely ordered rings. Also for a discretely ordered ring M and a real closed field R containing M we prove a theorem on the distribution of the discrete orderings of in in geometric terms. To be more precise, we prove that any ball in ) with center α and radius r (defined via Robson's metric) contains a discrete ordering of whenever r is positive non-infinitesimal and α is at infinite distance from all hyperplanes over M.
Download TeX format |
|
| back to top | |
