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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The conormal module of an almost complete intersection


Author: Ernst Kunz
Journal: Proc. Amer. Math. Soc. 73 (1979), 15-21
MSC: Primary 13F99; Secondary 14M10
MathSciNet review: 512049
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Abstract: The conormal module of an ideal I in a commutative ring S is the $ S/I$-module $ I/{I^2}$. Assume S is a regular noetherian ring and I a prime ideal, which is locally everywhere a complete intersection or an almost complete intersection (i.e. needs one generator more than in the complete intersection case). In this situation necessary and sufficient conditions for $ I/{I^2}$ being torsion free are given. Moreover the torsion of $ I/{I^2}$ is expressed in terms of Kähler differentials of $ S/I$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0512049-8
PII: S 0002-9939(1979)0512049-8
Keywords: Almost complete intersection, conormal module, canonical module, differential module, Dedekind and Kähler different, regular differential forms
Article copyright: © Copyright 1979 American Mathematical Society