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OPENNESS OF FID-LOCI

Published online by Cambridge University Press:  06 December 2006

RYO TAKAHASHI
RYO TAKAHASHI
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan email: takahasi@math.meiji.ac.jp
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Abstract

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Let $R$ be a commutative Noetherian ring and $M$ a finite $R$-module. In this paper, we consider Zariski-openness of the FID-locus of $M$, namely, the subset of $\mathrm{spec}\,R$ consisting of all prime ideals ${\mathfrak p}$ such that $M_{\mathfrak p}$ has finite injective dimension as an $R_{\mathfrak p}$-module. We prove that the FID-locus of $M$ is an open subset of $\mathrm{spec}\,R$ whenever $R$ is excellent.

Keywords

13D0513F40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 3 , September 2006 , pp. 431 - 435
Copyright
2006 Glasgow Mathematical Journal Trust