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 is finite. This generalizes the main result of Quy [10] and Brodmann and Lashgari [4].
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