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
JournalCommunications in Algebra
DOIs
Publication statusPublished - Jan 1 2019

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Direct Sum
Multiplicity
Module
Non-negative
Integer
Invariant
Generalization

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

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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.",
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KW - Hilbert–Samuel multiplicity

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