Document Type : Original Manuscript


1 Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.

2 Department of Mathematics, University of Tabriz, Tabriz, Iran; and School of Mathematics, Institute for research in fundamental sciences (IPM), P.O. Box 19395-5746, Tehran, Iran.


Let R be a commutative Noetherian ring, I, J be ideals of R such that
J ⊆ I, and M be a finitely generated R-module. In this paper, we prove that the
invariants AJI
(M) := inf{i ∈ N0 | JtHi
I (M) is not Artinian for all t ∈ N0} and inf{i ∈
N0 | JtHi
I (M) is not minimax for all t ∈ N0} are equal. In particular, we show that the
invariants AII
(M) and inf{i ∈ N0 | Hi
I (M) is not minimax} are equal. We also establish
the local-global principle, AJI
(M) = inf{AJRp
(Mp)|p ∈ Spec (R)}, in some cases.


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