Extension functors of cominimax modules

摘要

Let 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 i0, whenever M is I-cominimax and N is finitely generated with dim N2. Also, it is shown that the R-module graphic x is I-cominimax for all i0, whenever N is finitely generated and M is I-cominimax with dim M1. 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 i0 and j0. 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 i0, when one of the following statements holds: