### 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 language | English |
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Journal | Communications in Algebra |

DOIs | |

Publication status | Published - Jan 1 2019 |

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### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**A formula for the associated Buchsbaum–Rim multiplicities of a direct sum of cyclic modules II.** / Hayasaka, Futoshi.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A formula for the associated Buchsbaum–Rim multiplicities of a direct sum of cyclic modules II

AU - Hayasaka, Futoshi

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Buchsbaum–Rim function

KW - Buchsbaum–Rim multiplicity

KW - cyclic modules

KW - Hilbert–Samuel multiplicity

UR - http://www.scopus.com/inward/record.url?scp=85063933359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063933359&partnerID=8YFLogxK

U2 - 10.1080/00927872.2018.1555836

DO - 10.1080/00927872.2018.1555836

M3 - Article

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

ER -