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The homological degree of a module
Author(s):
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  is an extension of the usual notion of multiplicity tailored to provide a numerical signature for the module even when  is not Cohen-Macaulay. We construct a degree,  , 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:
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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