Abstract
ABSTRACTLet R be a commutative Noetherian ring with identity and I be an ideal of R. Also, let M and N be two nonzero R-modules. We prove that the R-module is I-cominimax for all i≥0, whenever M is I-cominimax and N is finitely generated with dim N ≤ 2. Also, it is shown that the R-module is I-cominimax for all i ≥ 0, whenever N is finitely generated and M is I-cominimax with dim M ≤ 1. As an immediate consequence, we obtain that if M is a nonzero minimax R-module such that , then for each finitely generated R-module N, is I-cominimax for all i ≥ 0 and j ≥ 0. Moreover, we prove that if R is local, M is I-cominimax and N is finitely generated, then the R-module is I-weakly cofinite for all i ≥ 0, when one of the following statements holds:(i) dim N = 3 or(ii) dim M ≤ 2.
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