Transactions of the American Mathematical Society

Author(s): Wolmer V. Vasconcelos
Journal: Trans. Amer. Math. Soc. 350 (1998), 1167-1179.
MSC (1991): Primary 13D40; Secondary 13D45, 13P10
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 13D40, 13D45, 13P10

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: 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
Copyright of article: Copyright 1998, American Mathematical Society

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