## The homological degree of a module

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- by Wolmer V. Vasconcelos
- Trans. Amer. Math. Soc.
**350**(1998), 1167-1179 - DOI: https://doi.org/10.1090/S0002-9947-98-02127-8
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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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## Bibliographic 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
- Received by editor(s): June 3, 1996
- Additional Notes: The author was partially supported by the NSF
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**350**(1998), 1167-1179 - MSC (1991): Primary 13D40; Secondary 13D45, 13P10
- DOI: https://doi.org/10.1090/S0002-9947-98-02127-8
- MathSciNet review: 1458335