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 ring with non-zero identity and m be a unital r-module. then the concept of quasi-secondary submodules of m is introduced and some results concerning this class of submodules is obtained

in this paper, we give a generalization of the integral dependence from rings to modules. we study the stability of the integral closure with respect to various module theoretic constructions. moreover, we introduce the notion of integral extension of a module and prove the lying over, going up and going down theorems for modules.

In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.

We define the notion of almost $n$-layered $QTAG$-modules and study their basic properties. One of the main result is that almost 1-layered modules are almost $(omega+1)$-projective exactly when they are almost direct sum of countably generated modules of length less than or equal to $(omega+1)$. Some other characterizations of this new class are also established.

Let $A$ be a Banach algebra, $\Omega(A)$ be the character space of $A$ and $\alpha\in\Omega(A)$. In this paper, we examine the characteristics of $\alpha$-projective (injective) $A$-modules and demonstrate that these character-based $A$-modules also satisfy well-known classical homological properties on Banach $A$-modules.

reservoir characterization plays an important role in different parts of an industrial project. the results from a reservoir characterization study give insight into rock and fluid properties which can optimize the choice of drilling locations and reduce risk and uncertainty. delineating hydrocarbon bearing zones within a reservoir is the main objective of any seismic reservoir characterization...

in this paper, applying the concept of generalized a-valued norm on a right h  - module and also the notion of ϕ-homomorphism of finsler modules over c  -algebras we rst improve the de nition of the finsler module over h  -algebra and then de ne ϕ-morphism of finsler modules over h  -algebras. finally we present some results concerning these new ones.

inspired by a recent work of buchweitz and flenner, we show that, for a semidualizing bimodule $c$, $c$--perfect complexes have the ability to detect when a ring is strongly regular.it is shown that there exists a class of modules which admit minimal resolutions of $c$--projective modules.

in this paper, we presented algebroids and crossed modules of algebroids. we also presented pullback crossed module of algebroids and we then define pushout crossed modules of algebroids.