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manuscripta mathematica

, Volume 22, Issue 3, pp 225–228 | Cite as

A remark on almost complete intersections

  • Yoichi Aoyama
Article

Abstract

Let k be a perfect field and S the quotient ring of a polynomial ring k[X1,...,Xt] with respect to a prime ideal. Let I be a prime ideal of S such that R=S/I is an almost complete intersection. Then, in his paper [2], Matsuoka proves that the homological dimension of the differential module ΩR/Kis infinite under the assumption that R is Cohen-Macaulay and I2 is a primary idea]. In this paper we prove that the result is valid without the above assumption.

Keywords

Number Theory Algebraic Geometry Prime Ideal Topological Group Complete Intersection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    KUNZ, E.: Almost complete intersections are not Gorenstein rings. J. Alg.28, 111–115 (1974)Google Scholar
  2. [2]
    MATSUOKA, T.: On almost complete intersections. to appear in manuscripta math.Google Scholar
  3. [3]
    VASCONCELOS, W. V.: A note on normality and the module of differentials. Math. Zeitschr.105, 291–293 (1968)Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Yoichi Aoyama
    • 1
  1. 1.Department of Mathmatics Faculty of ScienceEhime UniversityMatsuyamaJapan

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