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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotic periodicity of grade associated to multigraded modules
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by Futoshi Hayasaka PDF
Proc. Amer. Math. Soc. 140 (2012), 2279-2284 Request permission

Abstract:

Let $R$ be a Noetherian $\mathbb {N}^r$-graded ring generated in degrees $\textbf {d}_1, \dots , \textbf {d}_r$ which are linearly independent vectors over $\mathbb {R}$, and let $\mathfrak a$ be an ideal in $R_\textbf {0}$. In this paper, we investigate the asymptotic behavior of the grade of the ideal $\mathfrak a$ on the homogeneous components $M_\textbf {n}$ 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
  • Received by editor(s): February 22, 2011
  • Published electronically: November 8, 2011
  • Communicated by: Irena Peeva
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 2279-2284
  • MSC (2010): Primary 13A02; Secondary 13C15
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11370-4
  • MathSciNet review: 2898691