TY - JOUR

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

AU - Hayasaka, Futoshi

N1 - Publisher Copyright:
© 2019, © 2019 Taylor & Francis Group, LLC.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/8/3

Y1 - 2019/8/3

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 - Hilbert–Samuel multiplicity

KW - cyclic modules

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

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U2 - 10.1080/00927872.2018.1555836

DO - 10.1080/00927872.2018.1555836

M3 - Article

AN - SCOPUS:85063933359

SN - 0092-7872

VL - 47

SP - 3250

EP - 3263

JO - Communications in Algebra

JF - Communications in Algebra

IS - 8

ER -