Abstract. Let R denote a commutative Noetherian (not necessarily local) ring and let I be an ideal of R of dimension one. The main purpose of this note is to show that the category M (R, I)com of I-cominimax Rmodules forms an Abelian subcategory of the category of all R-modules. This assertion is a generalization of the main result of Melkersson in [15]. As an immediate consequence of this result we get some conditions for cominimaxness of local cohomology modules for ideals of dimension one. Finally, it is shown that the category C 1 B (R) of all R-modules of dimension at most one with finite Bass numbers forms an Abelian subcategory of the category of all R-modules.

Abstract. Let R be a commutative Noetherian ring, I an ideal of R and T be a non-zero I-cofinite R-module with dim(T ) ≤ 1. In this paper, for any finitely generated R-module N with support in V (I), we show that the R-modules Ext i R (T, N ) are finitely generated for all integers i ≥ 0. This immediately implies that if I has dimension one (i.e., dim R/I = 1), then Ext i R (H j I (M ), N ) is finitely generated for all integers i, j ≥ 0, and all finitely generated R-modules M and N , with Supp(N ) ⊆ V (I).

Let [Formula: see text] be a Noetherian local ring and [Formula: see text], [Formula: see text] be two finitely generated [Formula: see text]-modules. In this paper, it is shown that [Formula: see text] and [Formula: see text] for each [Formula: see text] and each integer [Formula: see text]. In particular, if [Formula: see text] then [Formula: see text]. Moreover, some applications of these results will be included.

Abstract. Let R be a commutative Noetherian regular local ring containing a field. Let I be an ideal of R and let` 0 be an integer. In this paper it is shown that for every finitely generated R-module M and each integer i `, the Bass numbers of the R-module H i I .M / are finite, whenever, dim Supp.H i I .R// Ä 1, for all i `.