The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .
Background: Fixed orthodontic appliances impede the maintenance of oral hygiene and result in plaque accumulation leads to enamel demineralization caused by acids produced by bacteria. Studies on plaque control strategies in orthodontic populations are limited. This might be caused by difficulties in the quantitative evaluation of dental plaque because the teeth have various levels of bracket coverage, and different tooth sizes and malocclusions, making the traditional categorical indices complex. The present study aims to evaluate the effect of different hygiene protocols on plaque quantity on bands with different attachments. Materials and method: Twenty patients had four bands within the orthodontic appliance. Then randomly divided into
... Show MoreThe study aims to indicate the role of the mechanisms and principles of corporate governance in the activation of social responsibility reports, and increase disclosure, to achieve sustainability, legitimacy, and integrity of the business. Through the presentation of the conceptual framework for corporate governance and social responsibility, identify the key dimensions of social responsibility and the statement of the relationship between the mechanisms of governance and social responsibility reports in accordance with these dimensions. To prove the hypothesis research has selected a sample of listed companies in the Iraqi market for securities,
... Show MoreA gamma T_ pure sub-module also the intersection property for gamma T_pure sub-modules have been studied in this action. Different descriptions and discuss some ownership, as Γ-module Z owns the TΓ_pure intersection property if and only if (J2 ΓK ∩ J^2 ΓF)=J^2 Γ(K ∩ F) for each Γ-ideal J and for all TΓ_pure K, and F in Z Q/P is TΓ_pure sub-module in Z/P, if P in Q.
In the present paper, a simply* compact spaces was introduced it defined over simply*- open set previous knowledge and we study the relation between the simply* separation axioms and the compactness, in addition to introduce a new types of functions known as 𝛼𝑆 𝑀∗ _irresolte , 𝛼𝑆 𝑀∗ __𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 and 𝑅 𝑆 𝑀∗ _ continuous, which are defined between two topological spaces.
In this paper mildly-regular topological space was introduced via the concept of mildly g-open sets. Many properties of mildly - regular space are investigated and the interactions between mildly-regular space and certain types of topological spaces are considered. Also the concept of strong mildly-regular space was introduced and a main theorem on this space was proved.
Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.
The main goal of this paper is to introduce and study a new concept named d*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d*-supplement submodule. Many relationships of d*-supplemented modules are studied. Especially, we give characterizations of d*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d*-supplemented and by an example we show that the converse is not true.
Let R be a ring with identity and M is a unitary left R–module. M is called J–lifting module if for every submodule N of M, there exists a submodule K of N such that
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.