Full paper in PDF:
$%J. J. Madden and N. Schwartz, Separating ideals in dimension 2, Rev. Mat. Univ. Complut. Madrid 10 (1997), supplementary, 217240. %$

Separating Ideals in Dimension 2
James J. MADDEN and Niels SCHWARTZ
Department of Mathematics
Louisiana State University
Baton Rouge LA 70803 USA
Fakultät für Mathematik und Informatik
Universität Passau
Postfach 2540
94030 Passau Germany

ABSTRACT

Experience shows that in geometric situations the separating ideal associated with two orderings of a ring measures the degree of tangency of the corresponding ultrafilters of semialgebraic sets. A related notion of separating ideals is introduced for pairs of valuations of a ring. The comparison of both types of separating ideals helps to understand how a point on a surface is approached by different half-branches of curves.

1991 Mathematics Subject Classification: 13A18, 14P99.