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On almost complete intersections

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Abstract

Let R be a local ring such that R=S/I where S is a regular local ring and I is a prime ideal of height r. In this paper it is shown that if I is minimally generated by r+1 elements, then there exists an R-homomorphism φ: KR→Rr+1 such that φ is an injection and Rr+1/φ(KR)≌I/I2 where KR:=Ext rS (R,S) the canonical module of R. Moreover, in case where S is a locality over a perfect field k, it is also shown that if R is Cohen-Macaulay and I2 is a primary ideal, then the homological dimension of the differential module ΩR/k is infinite.

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Authors and Affiliations

  1. Department of Mathematics Faculty of Sciences, Ehime University, Matsuyama, Japan

    Tadayuki Matsuoka

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  1. Tadayuki Matsuoka
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Additional information

The author wishes to thank his colleague Mr.Y.Aoyama for valuable discussions in connection with this subject.

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Matsuoka, T. On almost complete intersections. Manuscripta Math 21, 329–340 (1977). https://doi.org/10.1007/BF01167852

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  • DOI: https://doi.org/10.1007/BF01167852

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