An R-module M is called a polyform module if every essential submodule of M is rational. The main objective of this paper is to introduce a new concept of modules named fully polyform modules. This kind of module is contained in the class of polyform modules. We study in detail fully polyform modules, so several properties of this concept are investigated. Other characterizations and partial characterisations (i.e., satisfied by certain conditions) of the definition of fully polyform module analogous to those known in the concept of a polyform module are given and discussed. For instance, we proved that a module M is a fully polyform module if and only if M)=0 for each P-essential submodule N of M and for each V≤M with NÍVÍM. Relationships between this class of modules and some other related concepts are discussed such as monoform, QI-monoform, essentially quasi-Dedekind, essentially prime and St-polyform modules. Moreover, useful concepts and their influence or relationships with fully polyform modules such as P-uniform and Pe-prime modules are introduced.
Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.
The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.
A new family of nematic liquid crystal dendrimers derived from 3,5-dihydroxybenzoic acid were synthesized. The synthesis of the dendrimers compounds shows the influence of the dendritic core on the mesomorphic properties. The liquid crystalline properties were studied by polarizing optical microscopy (POM) equipped with a hot stage, the structures of the synthesized compounds characterized using FTIR and 1HNMR spectroscopy.
solid state reaction technique (SSR) was used to prepare high-Tc phase in superconductors the effect of additional Pb to was investigated it has been found
He mentioned in this article the main types of corruption, which are political, moral, financial and administrative. Others may add other types of corruption, such as religious, scientific, media, informational and statistical corruption. At the global level, the focus is largely on financial corruption, although other types of corruption are no less bad than it. Financial corruption can be defined as all financial deviations in violation of general laws or the provisions of regulations, legislation, and procedures regulating the work of the state, private institutions and individuals and applied in state institutions and the private sector in general and inconsistent with the controls and instructions of financial control.
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... Show MoreWe 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