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 report the discovery of TOI-1444b, a 1.4-$R_\oplus$ super-Earth on 0.47-day orbit around Sun-like star discovered by {\it TESS}. Precise radial velocities from Keck/HIRES confirmed planet and constrained mass to be $3.87 \pm 0.71 M_\oplus$. The RV dataset also indicates possible non-transiting, 16-day ($11.8\pm2.9M_\oplus$). tentative detection phase curve variation secondary eclipse TOI-144...

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...