A formula for the associated Buchsbaum–Rim multiplicities of a direct sum of cyclic modules II

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    Abstract

    The associated Buchsbaum–Rim multiplicities of a module are a descending sequence of non-negative integers. These invariants of a module are a generalization of the classical Hilbert–Samuel multiplicity of an ideal. In this article, we compute the associated Buchsbaum–Rim multiplicity of a direct sum of cyclic modules and give a formula for the second to last positive associated Buchsbaum–Rim multiplicity in terms of the ordinary Buchsbaum–Rim and Hilbert–Samuel multiplicities. This is a natural generalization of a formula given by Kirby and Rees.

    Original languageEnglish
    Pages (from-to)3250-3263
    Number of pages14
    JournalCommunications in Algebra
    Volume47
    Issue number8
    DOIs
    Publication statusPublished - Aug 3 2019

    Keywords

    • Buchsbaum–Rim function
    • Buchsbaum–Rim multiplicity
    • Hilbert–Samuel multiplicity
    • cyclic modules

    ASJC Scopus subject areas

    • Algebra and Number Theory

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