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On the Koszul homology modules for the powers of a multiplicity system

Part of: Local rings and semilocal rings

Published online by Cambridge University Press:  26 February 2010

J-L. García Roig  and
D. Kirby
J-L. García Roig
Affiliation:
Cruz Roja 26, 3°4a, Hospitalet, Barcelona, Spain.
D. Kirby
Affiliation:
Faculty of Mathematical Studies, The University, Southampton.
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Extract

It is well-known that if R is a commutative ring with identity, M is a Noetherian R-module and I is an ideal of R such that M/IM has finite length, then the function n → lR (M /InM) is a polynomial function for n large (cf. [3], p. II-25), where lR denotes length as an R-module. In this note we are concerned with the function

where a1, … , ar is a multiplicity system for has finite length.

MSC classification

Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
Type
Research Article
Information
Mathematika , Volume 33 , Issue 1 , June 1986 , pp. 96 - 101
Copyright
Copyright © University College London 1986

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References

1.Northcott, D. G.. Lessons on Rings, Moduiles and Multiplicities (Cambridge, 1968).CrossRefGoogle Scholar
2.Schenzel, P., Ngo Viet Trung and Nguyen Tu Cuong. Verallgemeinerte Cohen-Macaulay Moduln. Math. Nachr., 85 (1978), 57–73.CrossRefGoogle Scholar
1.Serre, J-P.. Algèbre locale: Multiplicités, Lecture Notes in Math. No. 11 (Springer, Berlin, 1975).Google Scholar
4.Stuckrad, J. and Vogel, W.. Eine Verallgemeinergung der Cohen-Macaulay Ringe und Anwendungen auf ein Problem der Multiplizitätstheorie. J. Math. Kyoto Univ., 13 (1973), 513–528.Google Scholar