The main objective of this thesis is to study new concepts (up to our knowledge) which are P-rational submodules, P-polyform and fully polyform modules. We studied a special type of rational submodule, called the P-rational submodule. A submodule N of an R-module M is called P-rational (Simply, N≤_prM), if N is pure and Hom_R (M/N,E(M))=0 where E(M) is the injective hull of M. Many properties of the P-rational submodules were investigated, and various characteristics were given and discussed that are analogous to the results which are known in the concept of the rational submodule. We used a P-rational submodule to define a P-polyform module which is contained properly in the polyform module. An R-module M is called P-polyform if every essential submodule of M is P-rational in M. We study this kind of module in some detail and introduced some characterizations of the P-polyform module and its relationships with some other modules. The third kind of module in this thesis is called fully polyform module, and it is contained in the class of polyform module. A module M is said to be fully polyform, if every P-essential submodule of M is rational in M, that is Hom_R(M/N, E(M))=0 for every P-essential submodule N of M. In fact, the class of fully polyform modules lies between polyform modules and essentially quasi-Dedekind modules. The main characteristics of fully polyform modules were investigated, and some characterizations of these types of modules were established. Furthermore, the relationships between this class and other related modules were examined.
We dealt with the nature of the points under the influence of periodic function chaotic functions associated functions chaotic and sufficient conditions to be a very chaotic functions Palace
We introduce some new generalizations of some definitions which are, supra closure converge to a point, supra closure directed toward a set, almost supra converges to a set, almost supra cluster point, a set supra H-closed relative, supra closure continuous functions, supra weakly continuous functions, supra compact functions, supra rigid a set, almost supra closed functions and supra perfect functions. And we state and prove several results concerning it
The research aims to focus on the human rights guarantees as they are subjected to continuous violations due to changes, wars and conflicts between nations and people, especially in the Arab world and the third world due to political, social, economic and environmental conditions and the failure of democratic tracks under the current reality.
Keyword: Human rights, Reality, Ambition.
the Reception and the Creative Reaction
Melatonin, a hormone synthesized mainly by the pineal gland, has been found in extra-pineal organs as well. It’s known as an organizer of circadian rhythms and more recently as an anti-oxidant. In addition to its role in maintaining immunity, pathophysiology of cardiovascular and neurological diseases, and as an anti-cancer agent, evidence has demonstrated that melatonin exerts a positive impact on male and female fertility primarily through oxygen scavenging effects. In In Vitro Fertilization (IVF) programs, supplementation of melatonin may be associated with better outcomes in terms of sperm quality, oocyte quality, embryo quality and pregnancy rates. This review summarizes various actions of melatonin on the body focusing on ma
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