in this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. in particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over noetherian rings are proved. moreover, w...

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...

Let $C$ be a semidualizing module over commutative Noetherian local ring $R$. In this paper we introduce new class of modules, namely $C$-canonical modules which are generalization canonical modules. It is shown that if the exists then and converse holds under special conditions. Also, characterization Gorenstein rings given via

In this note, we study commutative Noetherian local rings having finitely generated modules of finite Gorenstein injective dimension. In particular, we consider whether such rings are Cohen-Macaulay.

In this paper a generalized version of the Bass formula is proved for finitely generated modules of finite Gorenstein injective dimension over a commutative noetherian ring.

Let $R$ be a commutative Noetherian ring, $fa$ anideal of $R$ and $mathcal{D}(R)$ denote the derived category of$R$-modules. For any homologically bounded complex $X$, we conjecture that$sup {bf L}Lambda^{fa}(X)leq$ mag$_RX$. We prove thisin several cases. This generalize the main result of Hatamkhani and Divaani-Aazar cite{HD} for complexes.

We study the category of Sp-equivariant modules over infinite variable polynomial ring, where Sp denotes symplectic group. establish a number results about this category: for instance, we show that every finitely generated module M fits into an exact triangle $T \to F \to$ T is finite length complex torsion and "free" modules; determine Grothendieck group; (partially) structure injective module...