Extension functors of cominimax modules

Cominimaxness of local cohomology modules

“…One of the main results of this section is to prove that for an arbitrary ideal I of a Noetherian ring R, the category of I-cominimax FD 1 modules is an Abelian category. The following corollary is a generalization of [20], Theorem 3.4.…”

“…(See Theorem 2.11.) Using this fact we generalize [20], Corollary 3.5, as follows: Corrolary 1.6 (See Corollary 2.13). Let I be an ideal of a Noetherian ring R, M a nonzero minimax R-module such that H i I (M ) is FD 1 for all i 0.…”

“…Recently many authors have studied the minimaxness and cominimaxness of local cohomology modules and answered Conjecture 1.1 and Question 1.2 in the class of minimax modules in some cases (see [1], [7], [20], [22] [24], [26]). The purpose of this note is to make a suitable generalization of Conjecture 1.1 and Question 1.2 in terms of minimax modules instead of finitely generated modules.…”

Cominimaxness of certain general local cohomology modules

“…The general local cohomology module H j Φ (M ) is defined to be Φ-cominimax if there exists an ideal I ∈ Φ such that Ext i R (R/I, H j Φ (M )) is minimax, for all i, j ≥ 0. Recently many authors studied the minimaxness and cominimaxness of local cohomology modules and answered the Conjecture 1.1 and Question 1.2 in the class of minimax modules in some cases (see [1,3,9,14,24,27,29]). The purpose of this note is to make a suitable generalization of Conjecture 1.1 and Question 1.2 in terms of minimax modules instead of finitely generated modules for general local cohomology modules.…”

Abelian Category of Cominimax and Weakly Cofinite Modules

“…Since the concept of minimax modules is a natural generalization of the finitely generated modules, many authors studied the minimaxness and cominimaxness of local cohomology modules and answered the Hartshorne's question in the class of minimax modules (see for example [1,2,3,5,9,18,10,21]).…”