manuscripta mathematica

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

A remark on almost complete intersections

  • Yoichi Aoyama


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.


Number Theory Algebraic Geometry Prime Ideal Topological Group Complete Intersection 
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  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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