Abstract
Let (R, 𝔪) be a complete local ring, 𝔞 an ideal of R, and M a finitely generated R-module. The aim of this paper is to show that for any non-negative integer n, , where
is the nth finiteness dimension of M relative to 𝔞. As a consequence, it follows that the set
ACKNOWLEDGMENTS
The authors would like to thank Professors Hossein Zakeri and Kamal Bahmanpour for reading of the first draft and valuable discussions.
Notes
Communicated by S. Goto.