Let R be a commutative ring with unity .M an R-Module. M is called coprime module     (dual notion of prime module) if ann M =ann M/N for every proper submodule N of M   In this paper we study coprime modules we give many basic properties of this concept. Also we give many characterization of it under certain of module.

     Let  be an R-module, and let  be a submodule of . A submodule  is called -Small submodule () if for every submodule  of  such that  implies that . In our work we give the definition of -coclosed submodule and -hollow-lifiting modules with many properties.

  Let R be a commutative ring with unity. In this paper we introduce and study the concept of strongly essentially quasi-Dedekind module as a generalization of essentially quasiDedekind module. A unitary R-module M is called a strongly essentially quasi-Dedekind module if ( , ) 0 Hom M N M for all semiessential submodules N of M. Where a submodule N  of  an R-module  M  is called semiessential if , 0  pN for all nonzero prime submodules  P of  M .
 

Let R be an associative ring with identity. An R-module M is called generalized
amply cofinitely supplemented module if every cofinite submodule of M has an
ample generalized supplement in M. In this paper we proved some new results about
this conc- ept.

        he responsibility system has an important role in various international fields, including the area of ​​the proliferation of small and light weapons, and the destabilization and imbalance that this proliferation causes causes and legal centers, because without them, the agreement rules have no impact and significance, given the guarantees decided by the responsibility to ensure respect for the obligations imposed by that system,  Every action that violates the provisions of international law, whether it comes to a simple violation of an international obligation or a violation of a fundamental obligation that affects the interests of the international community requires the accountabilit

نظمت التشريعات محل الدراسة الحقوق الحزبية وفق شروط معينة ذات طبيعة موضوعية, حتى يمكن أن تمارس وتتحقق الغاية من إباحتها, غير أن هذا التنظيم أخرج فئات معينة من نطاق ممارسة هذه الحقوق, وعمل على فرض قيود معينة تبعاً لتوفر صفات معينة في الأشخاص الذين يعدون مواطنين وتنطبق عليهم الشروط العامة لممارسة الحقوق السياسية, فأصبحت الصفة الرسمية للمواطن في الدولة, وطبيعة الوظيفة, أو التكليف العام التي يمارسها, ومن شأنها أن

      The concept of semi-essential semimodule has been studied by many researchers.

     In this paper, we will develop these results by setting appropriate conditions, and defining new properties, relating to our concept, for example (fully prime semimodule, fully essential semimodule and semi-complement subsemimodule) such that: if for each subsemimodule of -semimodule  is prime, then  is fully prime. If every semi-essential subsemimodule of -semimodule  is essential then  is fully essential. Finally, a prime subsemimodule  of  is called semi-relative intersection complement (briefly, semi-complement) of subsemimodule  in , if , and whenever  with  is a prime subsemimodule in , , then .  Furthermore, some res

Let M be ,-ring and X be ,M-module, Bresar and Vukman studied orthogonal
derivations on semiprime rings. Ashraf and Jamal defined the orthogonal derivations
on -rings M. This research defines and studies the concepts of orthogonal
derivation and orthogonal generalized derivations on ,M -Module X and introduces
the relation between the products of generalized derivations and orthogonality on
,M -module.