A note on the Buchsbaum-Rim multiplicity of a parameter module

Futoshi Hayasaka; Eero Hyry

doi:10.1090/S0002-9939-09-10119-3

A note on the Buchsbaum-Rim multiplicity of a parameter module

Futoshi Hayasaka, Eero Hyry

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this article we prove that the Buchsbaum-Rim multiplicity e(F/N) of a parameter module N in a free module F=A^r is bounded above by the colength ℓ_A(F/N). Moreover, we prove that once the equality ℓ_A(F/N) = e(F/N) holds true for some parameter module N in F,then the base ring A is Cohen-Macaulay.

Original language	English
Pages (from-to)	545-551
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-09-10119-3
Publication status	Published - Feb 2010
Externally published	Yes

Keywords

Buchsbaum-Rim multiplicity
Euler-Poincaréchar- acteristic
Generalized Koszul complex
Parameter module

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-09-10119-3

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abstract = "In this article we prove that the Buchsbaum-Rim multiplicity e(F/N) of a parameter module N in a free module F=Ar is bounded above by the colength ℓA(F/N). Moreover, we prove that once the equality ℓA(F/N) = e(F/N) holds true for some parameter module N in F,then the base ring A is Cohen-Macaulay.",

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AU - Hyry, Eero

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AB - In this article we prove that the Buchsbaum-Rim multiplicity e(F/N) of a parameter module N in a free module F=Ar is bounded above by the colength ℓA(F/N). Moreover, we prove that once the equality ℓA(F/N) = e(F/N) holds true for some parameter module N in F,then the base ring A is Cohen-Macaulay.

KW - Buchsbaum-Rim multiplicity

KW - Euler-Poincaréchar- acteristic

KW - Generalized Koszul complex

KW - Parameter module

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A note on the Buchsbaum-Rim multiplicity of a parameter module

Abstract

Keywords

ASJC Scopus subject areas

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