On the Asymptotic Behavior of the Bass Numbers of Modules

Abstract

Let (R, 𝔪) be a Noetherian Gorenstein local ring and I be a principal ideal of R. In this article we show that the Bass numbers of the R-modules R/I ⁿ take constant values for large n.

Key Words:

• Bass numbers
• Gorenstein local ring
• Regular sequence

2010 Mathematics Subject Classification:

• 14B15
• 13E05

ACKNOWLEDGMENTS

The authors are deeply grateful to the referee for his/her careful reading of the article and valuable suggestions. Also, we would like to thank the Islamic Azad University-Ardabil Branch for its financial support.

Notes

Communicated by M. Cohen.