Asymptotic periodicity of grade associated to multigraded modules
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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.References
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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