In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule  of an R-module  is called Pr- maximal if  ,for any submodule  of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule  

 of an R-module  is named near (N-maximal) whensoever  is pure submodule of  such that  then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of  is Pr-maximal. A ring  is named Pr-ring if whole proper ideal of  is a Pr-maximal ideal, we offer the concept pure local (Pr-loc

In this paper, we introduce a new concept named St-polyform modules, and show that the class of St-polyform modules is contained properly in the well-known classes; polyform, strongly essentially quasi-Dedekind and ?-nonsingular modules. Various properties of such modules are obtained. Another characterization of St-polyform module is given. An existence of St-polyform submodules in certain class of modules is considered. The relationships of St-polyform with some related concepts are investigated. Furthermore, we introduce other new classes which are; St-semisimple and ?-non St-singular modules, and we verify that the class of St-polyform modules lies between them.

In this paper we investigated some new properties of π-Armendariz rings and studied the relationships between π-Armendariz rings and central Armendariz rings, nil-Armendariz rings, semicommutative rings, skew Armendariz rings, α-compatible rings and others. We proved that if R is a central Armendariz, then R is π-Armendariz ring. Also we explained how skew Armendariz rings can be ?-Armendariz, for that we proved that if R is a skew Armendariz π-compatible ring, then R is π-Armendariz. Examples are given to illustrate the relations between concepts.

    Let R be a commutative ring with identity, and M be a left untial module. In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L. Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied. Furthermore, modules with chain condition on w-closed submodules are studied.   

The concept of Justice in the Ancient western political thought The title of research is the concept of Justice in the ancient western political heritage. It includes the definition of the idea of Justice as well as its evolution and relation to the Law the study discussed two main period . the first one was regarding the concept of Justice in the Greek political thought ( sophists ,Socrates , plato , Aristotle ,Epicureans , and stoics ) . While the second ocused on the concept of justice in Roman political thought Via their great thinkers as polypus and Cicero .

Designed Mirrors double and triple package adoption concept heap where they were changing the thickness of the layers within periodic basis of the pile and different ratios (p: q) in addition to change the refractive index of materials within periodic basis and its impact on sites Dhour tops high reflectivity study included spectral region visible and infrared, depending on NdharahFeatured matrix adjusted fall of light close to the vertical arrangement multilayer dielectric materials and thin films homogeneous and uniform

Death is undoubtedly the theme of Don DeLillo’s White Noise. Murray Siskind, a College-on-the-Hill professor who is obsessed with the exploration and reinterpretation of American popular culture, talks about the Tibetan Book of the Dead, and the German mentor of Jack Gladney has been using the Egyptian Book of the Dead, translated into German. The core episode of the story is the Airborne Toxic Event, the associate of Heinrich (Jack’s teenage son), Orestes Mercator, dreams of becoming one of the great figures in the Guinness Book by challenging and confronting death by enclosing himself in a glass pen jam-packed with poisonous snakes, and Heinrich challenges an imprisoned mass murderer in a chess game. The scholarly expertise of Jack c

Presupposition, which indicates a prior assumption, is a vital notion in both semantic and pragmatic disciplines. It refers to assumptions implicitly made by interlocutors, which are necessary for the correct interpretation of an utterance. Although there is a general agreement that presupposition is a universal property of Language, there are various propositions concerning its nature. However, this research work proposes that presupposition is a contextual term, thus, is more pragmatic than semantic in its nature.Although Semantics and Pragmatics are two distinct disciplines, they are interrelated and complementary to each other, since meaning proper involves both, and since there is no clear borderline between the two disciplines. How

Let S be a prime inverse semiring with center Z(S). The aim of this research is to prove some results on the prime inverse semiring with (α, β) – derivation that acts as a homomorphism or as an anti- homomorphism, where α, β are automorphisms on S.