Abstract
Let (R, 𝔪) be a Noetherian local ring I, J two ideals of R and M a finitely generated R-module. Let k ≥ −1 and r
k
= depth
k
(I, J
n
M/J
n+1
M) be the length of a maximal (J
n
M/J
n+1
M)-sequence in dimension >k in I defined by Brodmann and Nhan [Citation4]. It is first shown that r
k
becomes independent of n for large n. Then we prove in this article that the sets with k = −1 or k = 0, and
are stable for large n. We also obtain similar results for modules M/J
n
M.
ACKNOWLEDGMENT
This work is supported partly by the National Foundation for Science and Technology Development (Nafosted) of Vietnam.
Notes
Communicated by A. Singh.