Lifting modules plays important roles in module theory. H-supplemented are a nice generalization of lifting which have been studied extensively recently. In this article, we introduce proper via images fully invariant submodules. Let F be submodule right Rmodule M. We say that M is IF -H-supplemented case for every endomorphism φ M, there direct summand D such φ(F) + X = if and only It proved d...

The aim of this paper is to investigate generalizations locally artinian supplemented modules in module theory, namely radical and strongly modules. We have obtained elementary features for them. Also, we characterized by left perfect rings. Finally, proved that the reduced part a $R$-module has same property over Dedekind domain $R$.

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

A module M is called ?-?ss-supplemented if every submodule X of has a ?ss-supplement Y in which direct summand such that + = and ? Soc? (Y) where Soc?(Y) the sum simple ?-small submodules Y? for some M. Moreover, completely ?-?ss-supplemented. Thus, we present two new types algebraic structures are stronger than ?-D11 ?-D+11-modules, respectively. In this paper investigate basic properties, dec...

In mid-2004, it was decided that the list of optional modules available to students taking the MSc programme in Computing, Internet Law and Management at King’s College London (KCL) should be supplemented with a module in computer forensics (CF) and cybercrime. It was proposed that this module should be delivered as a reading course to be assessed by means of a dissertation and a linked viva vo...

We study syndetic sensitivity and mean for linear dynamical systems. For the aspect, we obtain some properties of adjoint operators left multiplication operators. also show that there exists a system (X×Y,T×S) such is cofinitely sensitive but (X,T) (Y,S) are not syndetically sensitive. if sensitive, where Y complex Banach space, spectrum T meets unit circle. results regarding perturbations.