Extensions of local domains with trivial generic fiber
Heinzer, William ; Rotthaus, Christel ; Wiegand, Sylvia
Illinois J. Math., Tome 51 (2007) no. 3, p. 123-136 / Harvested from Project Euclid
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We consider injective local maps from a local domain $R$ to a local domain $S$ such that the generic fiber of the inclusion map $R \hookrightarrow S$ is trivial, that is, $P \cap R \ne (0)$ 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 $R \hookrightarrow S$ having this property, we give some results on the dimension of $S$; in some cases we show $\dim S = 2$ and in some cases $\dim S = 1$.
Publié le : 2007-01-15
Classification:  13B02,  13A15,  13F25,  13J05 
@article{1258735328,
     author = {Heinzer, William and Rotthaus, Christel and Wiegand, Sylvia},
     title = {Extensions of local domains with trivial generic fiber},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 123-136},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258735328}
}

Heinzer, William; Rotthaus, Christel; Wiegand, Sylvia. Extensions of local domains with trivial generic fiber. Illinois J. Math., Tome 51 (2007) no. 3, pp.  123-136. http://gdmltest.u-ga.fr/item/1258735328/