Illinois Journal of Mathematics

Extensions of local domains with trivial generic fiber

William Heinzer, Christel Rotthaus, and Sylvia Wiegand

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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 $\dim S = 1$.

Article information

Source
Illinois J. Math., Volume 51, Number 1 (2007), 123-136.

Dates
First available in Project Euclid: 20 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258735328

Digital Object Identifier
doi:10.1215/ijm/1258735328

Mathematical Reviews number (MathSciNet)
MR2346190

Zentralblatt MATH identifier
1129.13007

Subjects
Primary: 13B02: Extension theory
Secondary: 13A15: Ideals; multiplicative ideal theory 13F25: Formal power series rings [See also 13J05] 13J05: Power series rings [See also 13F25]

Citation

Heinzer, William; Rotthaus, Christel; Wiegand, Sylvia. Extensions of local domains with trivial generic fiber. Illinois J. Math. 51 (2007), no. 1, 123--136. doi:10.1215/ijm/1258735328. https://projecteuclid.org/euclid.ijm/1258735328


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