Nebraska Cooperative Fish & Wildlife Research Unit


Date of this Version

Spring 2007


2007 University of Illinois


Illinois Journal of Mathematics Volume 51, Number 1, Spring 2007, Pages 123–136 S 0019-2082


We consider injective local maps from a local domain R to a local domain S such that the generic fiber of the inclusion map R -> S is trivial, that is P R (0) for every nonzero prime ideal P of S. We present several examples of injective local maps involving power series that have or fail to have this property. For an extension R -> S having this property, we give some results on the dimension of S; in some cases we show dim S = 2 and in some cases dim S = 1.