A numerical characterization of reduction for arbitrary modules
نویسندگان
چکیده
Let (R,m) be a d-dimensional Noetherian local ring and E a finitely generated R-submodule of a free module R. In this work we introduce a Buchsbaum-Rim multiplicity sequence ck(E), k = 0, . . . , d + p − 1 for E that generalize the Buchsbaum-Rim multiplicity defined when E has finite colength in R as well as the Achilles-Manaresi multiplicity sequence that applies when E ⊆ R is an ideal. Our main result is that the new Buchsbaum-Rim multiplicity sequence can indeed be used to detect integral dependence of modules. Our proof is self-contained and implies known numerical criteria for integral dependence of ideals and modules.
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تاریخ انتشار 2006