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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The homological degree of a module


Author: Wolmer V. Vasconcelos
Journal: Trans. Amer. Math. Soc. 350 (1998), 1167-1179
MSC (1991): Primary 13D40; Secondary 13D45, 13P10
MathSciNet review: 1458335
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Abstract: A homological degree of a graded module $M$ is an extension of the usual notion of multiplicity tailored to provide a numerical signature for the module even when $M$ is not Cohen-Macaulay. We construct a degree, $\operatorname{hdeg}(M)$, that behaves well under hyperplane sections and the modding out of elements of finite support. When carried out in a local algebra this degree gives a simulacrum of complexity à la Castelnuovo-Mumford's regularity. Several applications for estimating reduction numbers of ideals and predictions on the outcome of Noether normalizations are given.


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Additional Information

Wolmer V. Vasconcelos
Affiliation: Department of Mathematics - Hill Center, Rutgers University, 110 Frelinghuysen RD, Piscataway, New Jersey 08854-8019
Email: vasconce@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02127-8
PII: S 0002-9947(98)02127-8
Keywords: Arithmetic degree, Castelnuovo-Mumford regularity, geometric degree, Gorenstein ring, homological degree, reduction number
Received by editor(s): June 3, 1996
Additional Notes: The author was partially supported by the NSF
Article copyright: © Copyright 1998 American Mathematical Society