Geodesic
OPENNESS OF FID-LOCI
Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 431-435

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DOI

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.
DOI : 10.1017/S0017089506003168
Mots-clés : 13D05, 13F40 
TAKAHASHI, RYO. OPENNESS OF FID-LOCI. Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 431-435. doi: 10.1017/S0017089506003168
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     title = {OPENNESS {OF} {FID-LOCI}},
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     year = {2006},
     volume = {48},
     number = {3},
     doi = {10.1017/S0017089506003168},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003168/}
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