Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

‎A module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some gen...

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $R$.  In this paper we  study the relationship between an$R$-module $M_R$ and the  general polynomial module  $M[x]$ over theskew polynomial ring $R[x;alpha,delta]$. We introduce the notionsof skew-Armendariz modules and skew quasi-Armendariz modules whichare generalizations of $alpha$-Armendariz modules and extend thecla...

The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.

We develop a duality for operations on nested pairs of modules that generalizes the between absolute interior and residual closure from [5], extending our previous results to expanded context. apply this in particular integral basically full closures their respective cores obtain empty interiors hulls. also dualize some known formulas core an ideal hull submodule injective residue field. The ar...

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...

We define for arbitrary modules over a finite von Neumann algebra A a dimension taking values in [0,∞] which extends the classical notion of von Neumann dimension for finitely generated projective A-modules and inherits all its useful properties such as Additivity, Cofinality and Continuity. This allows to define L2-Betti numbers for arbitrary topological spaces with an action of a discrete gro...

Abstract Fisher [10] and Baur [6] showed independently in the seventies that if T is a complete first-order theory extending of modules, then class models with pure embeddings stable. In [25, 2.12], it asked same true for any abstract elementary $(K, \leq _p)$ such K modules $\leq _p$ submodule relation. this paper we give some instances where true: Theorem. Assume R an associative ring unity. ...