Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

This paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.

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

The research aims to measure the impact of the quality of the audit on the Earnings Quality, for a sample of private joint stock companies listed on the Iraq Stock Exchange, as the research sample included (14) private and listed joint stock companies in issuing their financial statements for the period from (2010-2018), as well as companies The audit offices in charge of auditing these companies, which number (18) companies or an audit office, and the research relied on two main models for measurement, as the first model reflects the assumed relationship between independent variables represented in the characteristics of external audit quality and measuring the extent of its impact on the dependent variable represented in the Ea

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 commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Five samples of the ternary alloy Ge-S-Cd were created using the melting point method, and the effects of partially substituting cadmium for germanium were determined. and partial substitution of germanium by cadmium was used to study the change in electrical conductivity. Electrical experiments were performed on Ge_35-xS₆₅Cd_xternary alloy with x = 0, 5, 10, 15, and 20. It was discovered that the conductivity (σ_dc) rises with rising temperature in all samples under experiment. This confirms that the samples have semiconductor behavior. It has been observed that there are three regions of electrical conductivity in the electrical conductivity curve at low, moderate, and high temperatures. The pr

The concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies this concept and it is relationship to previous generalizationsm especially  2-Absorbing submodule and Quasi-2-Absorbing submodule, in addition to studying the most important Propositions, charactarizations and Examples. Now in this research, which is considered a continuation of the definition that was presented earlier, which is the Extend Nearly Pseudo Quasi-2-Absorbing submodules, we have completed the study of this concept in multiplication modules. And the relationship between the Extend Nearly Pseudo Quasi-2-Absorbing submodule and Extend Nearly Pseudo Quasi-2-Abs

Abstract Throughout this paper R represents commutative ring with identity and M is a unitary left R-module, the purpose of this paper is to study a new concept, (up to our knowledge), named St-closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties of St-closed submodules are considered.

The present study deals with prepositions in the patterns of analytical unite of modern Russian language out of the functional -semantic aspects, which enhances the lexical semantics.  The study, also, sheds light on the prepositions of semantic derivation that adds value to the meaning of the unites, promotes the appearance of new forms that match the more important diverse complex analytical unit.

В статье рассмотрены отыменные предлоги в системе литических единиц русского языка с позиций функционального и семантического аспектов. Репрезентирована специфика функциониров