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Paper   IPM / M / 16203
School of Mathematics
  Title:   Discrete orderings in the real spectrum
  Author(s):  Shahram Mohsenipour
  Status:   Published
  Journal: J. Algebra
  Vol.:  560
  Year:  2020
  Pages:   1-16
  Supported by:  IPM
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.

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