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On openness of $ H\sb{n}$-locus and semicontinuity of $ n$th deviation

Author: Alfio Ragusa
Journal: Proc. Amer. Math. Soc. 80 (1980), 201-209
MSC: Primary 13D03; Secondary 13H10
MathSciNet review: 577744
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Abstract: M. André has used the property $ {H_n}$, namely the vanishing of certain homology groups, and the deviation $ {\delta _n}$ to characterize some classes of rings. In the present paper the author establishes an inequality on the deviations and obtains a Nagata criterion for $ {H_n}$-locus and its openness for quotients of complete intersection rings and excellent rings. The upper-semicontinuity for $ {\delta _n}$ is also proved for the same classes of rings.

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