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.
@article{urn:eudml:doc:44261,
title = {Separating ideals in dimension 2.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {10},
year = {1997},
pages = {217-240},
zbl = {0942.13022},
mrnumber = {MR1485301},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44261}
}
Madden, James J.; Schwartz, Niels. Separating ideals in dimension 2.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 217-240. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44261/