The concept of a 2-Absorbing submodule is considered as an essential feature in the field of module theory and has many generalizations. This articale discusses the concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules and their relationship to the 2-Absorbing submodule, Quasi-2-Absorbing submodule, Nearly-2-Absorbing submodule, Pseudo-2-Absorbing submodule, and the rest of the other concepts previously studied. The relationship between them has been studied, explaining that the opposite is not true and that under certain conditions the opposite becomes true. This article aims to study this concept and gives the most important propositions, characterizations, remarks, examples, lemmas, and observations related to it. In the en

        In this article, unless otherwise established, all rings are commutative with identity and all modules are unitary left R-module. We offer this concept of WN-prime as new generalization of weakly prime submodules. Some basic properties of weakly nearly prime submodules are given. Many characterizations, examples of this concept are stablished.

A non-zero submodule N of M is called essential if N L for each non-zero submodule L of M. And a non-zero submodule K of M is called semi-essential if K P for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ⊊ W ⊆ M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ? W ? M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of ri

  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 a commutative ring with identity and let M be a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of semi-essential submodules which introduced by Ali S. Mijbass and Nada K. Abdullah, and we make simple changes to the definition relate with the zero submodule, so we say that a submodule N of an R-module M is called semi-essential, if whenever N ∩ P = (0), then P = (0) for each prime submodule P of M. Various properties of semi-essential submodules are considered.

  In this paper, we introduce and study the concept of S-coprime submodules, where a proper submodule N of an R-module M is called S-coprime submodule if M N is S-coprime Rmodule. Many properties about this concept are investigated.

      Let  be a right module over a ring  with identity. The semisecond submodules are studied in this paper. A nonzero submodule  of   is called semisecond if    for each . More information and characterizations about this concept is provided in our work.