… the first section we bring some characterization of cofinite modules. … In this section we bring
some characterizations of cofinite modules… Now we extend this result for FA and AF modules. …

… In fact we show that a module M which is cofinite with respect to some ideal must satisfy some
… We begin by showing in Theorem 1·1 the striking result that cofiniteness of a module with …

… We are however avoiding the use of spectral sequences completely in this work, even if we
can show some of our results with this technique. So we provide an elementary proof of the …

… Furthermore, using [12, Theorem 4.1], Delfino [4] proved that if R is a complete local
domain under some mild conditions then the similar results hold. Also, Delfino and Marley [5, …

… We also prove a cofiniteness result about H;(M), where M is a finitely generated R-module …
for some positive integer n and some finitely generated module K. This gives the long exact …

… Now, for each R-module M we define q ( I , M ) = M - cd ( I , M ) , where M denotes the Serre
… I-cofinite R-modules. Our main goal in section 3 of this paper is to establish some results for …

… n} $$ R $-module for all $ i\leq {2-n} $. We conclude with some ordinary $\mathfrak {a} $-cofiniteness
results for local cohomology modules $\operatorname {H}^{i} _ {\mathfrak {a}}(X) $. …

… cocomplement (of some submodule) in M. Section 2 is devoted to the propositions about
cocomplements in a module. It is … Thus, in Section 4, we obtain the following result (Proposition …

… Note that (a, R)-cofinite is the classical a-cofinite. In the following we establish some
results on (a, M)-cofinite modules. The proofs of the following two results are classical. …

… Question 1: Whether the category C ( R , I ) cof of I-cofinite modules is an Abelian … I-cofinite
R-modules M with dim M ≤ 1 is Abelian. For some other similar results, see also [Citation1]. …