Asymptotic Periodicity of Primes Associated to Multigraded Modules

Abstract

In this paper, we investigate the asymptotic behavior of the set of primes associated to a graded ring extension of Noetherian multigraded rings and modules, and prove that the periodicity occurs in a cone. We also prove the same asymptotic behavior of the grade. The previous known results on this subject are recovered as a special case.

Key Words:

• Associated prime
• Cone
• Grade
• Module
• Multigraded

2010 Mathematics Subject Classification:

• Primary: 13A02
• Secondary: 13C15

ACKNOWLEDGMENTS

The author would like to thank the referee for his/her comments and suggestions.

This work was partially supported by Grant-in-Aid for Young Scientists (B) 22740027.

Notes

Communicated by I. Swanson.