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Spring 2007 Extensions of local domains with trivial generic fiber
William Heinzer, Christel Rotthaus, Sylvia Wiegand
Illinois J. Math. 51(1): 123-136 (Spring 2007). DOI: 10.1215/ijm/1258735328

Abstract

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 $\dim S = 1$.

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William Heinzer. Christel Rotthaus. Sylvia Wiegand. "Extensions of local domains with trivial generic fiber." Illinois J. Math. 51 (1) 123 - 136, Spring 2007. https://doi.org/10.1215/ijm/1258735328

Information

Published: Spring 2007
First available in Project Euclid: 20 November 2009

zbMATH: 1129.13007
MathSciNet: MR2346190
Digital Object Identifier: 10.1215/ijm/1258735328

Subjects:
Primary: 13B02
Secondary: 13A15, 13F25, 13J05

Rights: Copyright © 2007 University of Illinois at Urbana-Champaign

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Vol.51 • No. 1 • Spring 2007
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