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.
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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.