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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic periodicity of grade associated to multigraded modules


Author: Futoshi Hayasaka
Journal: Proc. Amer. Math. Soc. 140 (2012), 2279-2284
MSC (2010): Primary 13A02; Secondary 13C15
Published electronically: November 8, 2011
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Abstract: Let $ R$ be a Noetherian $ \mathbb{N}^r$-graded ring generated in degrees
$ {\bf d}_1, \dots , {\bf d}_r$ which are linearly independent vectors over $ \mathbb{R}$, and let $ \mathfrak{a}$ be an ideal in $ R_{\bf0}$. In this paper, we investigate the asymptotic behavior of the grade of the ideal $ \mathfrak{a}$ on the homogeneous components $ M_{\bf n}$ of a finitely generated $ \mathbb{Z}^r$-graded $ R$-module $ M$ and show that the periodicity occurs in a cone.


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Additional Information

Futoshi Hayasaka
Affiliation: Department of Liberal Arts and Sciences, Kagoshima National College of Technology, 1460-1 Shinko, Hayato-cho, Kirishima-shi, Kagoshima 899-5193, Japan
Email: hayasaka@kagoshima-ct.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11370-4
PII: S 0002-9939(2011)11370-4
Keywords: Module, multigraded, grade, cone
Received by editor(s): February 22, 2011
Published electronically: November 8, 2011
Communicated by: Irena Peeva
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.