Asymptotic periodicity of grade associated to multigraded modules

Futoshi Hayasaka

doi:10.1090/S0002-9939-2011-11370-4

Asymptotic periodicity of grade associated to multigraded modules

Futoshi Hayasaka

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

2 Citations (Scopus)

Abstract

Let R be a Noetherian ℕ ^r-graded ring generated in degrees d ₁,..., d _r which are linearly independent vectors over ℝ, and let a be an ideal in R ₀. In this paper, we investigate the asymptotic behavior of the grade of the ideal a on the homogeneous components M _n of a finitely generated ℤ ^r-graded R-module M and show that the periodicity occurs in a cone.

Original language	English
Pages (from-to)	2279-2284
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	140
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-2011-11370-4
Publication status	Published - 2012
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-2011-11370-4

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abstract = "Let R be a Noetherian ℕ r-graded ring generated in degrees d 1,..., d r which are linearly independent vectors over ℝ, and let a be an ideal in R 0. In this paper, we investigate the asymptotic behavior of the grade of the ideal a on the homogeneous components M n of a finitely generated ℤ r-graded R-module M and show that the periodicity occurs in a cone.",

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AB - Let R be a Noetherian ℕ r-graded ring generated in degrees d 1,..., d r which are linearly independent vectors over ℝ, and let a be an ideal in R 0. In this paper, we investigate the asymptotic behavior of the grade of the ideal a on the homogeneous components M n of a finitely generated ℤ r-graded R-module M and show that the periodicity occurs in a cone.

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Asymptotic periodicity of grade associated to multigraded modules

Abstract

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