The homological degree of a module

Vasconcelos, Wolmer

doi:10.1090/S0002-9947-98-02127-8

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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