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Fall 1998 Note on Birational Extensions in D-Dimension
Mee-Kyoung Kim
Missouri J. Math. Sci. 10(3): 153-158 (Fall 1998). DOI: 10.35834/1998/1003153


Let $(R,m)$ be a $d$-dimensional regular local ring with quotient field $K$ and $(S,n)$ be a $d$-dimensional normal local domain birationally dominating $R$ with $l(mS) = d$. In this paper, it is shown that the following three properties hold.

  1. $S$ is dominated by the $m$-adic prime divisor of $R$;

  2. $n^i \cap R = m^i$, for all $i \ge 1$;

  3. $R/m = S/n$.


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Mee-Kyoung Kim. "Note on Birational Extensions in D-Dimension." Missouri J. Math. Sci. 10 (3) 153 - 158, Fall 1998.


Published: Fall 1998
First available in Project Euclid: 23 November 2019

zbMATH: 1097.13502
MathSciNet: MR1651233
Digital Object Identifier: 10.35834/1998/1003153

Rights: Copyright © 1998 Central Missouri State University, Department of Mathematics and Computer Science

Vol.10 • No. 3 • Fall 1998
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