let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

let $r$ be a commutative noetherian ring with non-zero identity, $fa$ an ideal of $r$, and $x$ an $r$--module. here, for fixed integers $s, t$ and a finite $fa$--torsion $r$--module $n$, we first study the membership of $ext^{s+t}_{r}(n, x)$ and $ext^{s}_{r}(n, h^{t}_{fa}(x))$ in the serre subcategories of the category of $r$--modules. then, we present some conditions which ensure the exi...

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary  generalized local cohomology  modules.  Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$  are  finitely generated  $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...

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let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigate some properties of formal local cohomology modules with respect to a serre subcategory. we provide a common language to indicate some properties of formal local cohomology modules. let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigat...

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

let $r$ be a commutative noetherian ring with non-zero identity and $fa$ an ideal of $r$. let $m$ be a finite $r$--module of finite projective dimension and $n$ an arbitrary finite $r$--module. we characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(m,n)$ in certain serre subcategories of the category of modules from upper bounds. we define and study the properti...

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then there exists an ideal a of R such that AttR Hna (M)=T. As an application, we give some relationships between top local cohomology modules and top f...