Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
MathSciNet review: 2898691
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 13A02, 13C15

Retrieve articles in all journals with MSC (2010): 13A02, 13C15

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

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.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia