In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.

Let R be a commutative ring with identity, and let M be a unity R-module. M is called a bounded R-module provided that there exists an element x?M such that annR(M) = annR(x). As a generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element x?M such that . In this paper, some properties and characterizations of semi-bounded modules are given. Also, various basic results about semi-bounded modules are considered. Moreover, some relations between semi-bounded modules and other types of modules are considered.

تُعبّرُ الصُّورةُ الحسَّيةُ في شعرِ ابن دُنَينير الموصليِّ^([i]) في بنيتها عن تجربةِ الشاعرِ الوجدانيةِ والذهنيةِ, وأفكارهِ ومشاعرِهِ؛ فيصوغُ بها مَفهومًا جديدًا للواقعِ الماديِّ والمعنويِّ، الذي يتسمُ بالوضوحِ أولاً، وبالقرْبِ من الذهنِ ثانيًا، للربْطِ بين الحواسِّ الإنسانيةِ والمعاني الذهنيةِ، لِتُقَدِّمَ الصُّورةُ الحسيَّةُ إلى ((المتلقي صُورًا مرئيةً، يُعادُ تشكيلُها سياق

The topological parameters of the metal-metal and metal-ligand bonding interactions in a trinuclear tetrahydrido cluster [(Cp*Co) (CpRu)2 (μ3-H) (μ-H)3]1 (Cp* = η5 -C5Me4Et), (Cp = η5 -C5Me5), was explored by using the Quantum Theory of Atoms-in-Molecules (QTAIM). The properties of bond critical points such as the bond delocalization indices δ (A, B), the electron density ρ(r), the local kinetic energy density G(r), the Laplacian of the electron density ∇2ρ(r), the local energy density H(r), the local potential energy density V(r) and ellipticity ε(r) are compared with data from earlier organometallic system studies. A comparison of the topological processes of different atom-atom interactions has become possible than

    Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as  we discuss the relation between this concept and some other related concepts.

Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.

Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.