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.
Abstract In this work we introduce the concept of approximately regular ring as generalizations of regular ring, and the sense of a Z- approximately regular module as generalizations of Z- regular module. We give many result about this concept.
In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules. We also give some results and properties of this new kind of modules.
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This study was carried out to find out the effect of germination of broad beans and chickpeas seeds for different periods on the sensory properties of homus bethina and falafel. The results revealed that the studied properties were significantly different (P<0.05) in tenderness, flavor and overall acceptance as compared to control samples. While other properties such as appearance, body (texture), leavening and color did not showed significant differences.It was found that treatment B1 (100% germinated broad beans) varied significantly in tenderness in comparison with control samples.Treatment B3 (75% ordinary bread beans + 25% germinated broad beans) revealed significant differences (P<0.05) in both flavor and overall acceptance as compar
... Show MoreSuppose that F is a reciprocal ring which has a unity and suppose that H is an F-module. We topologize La-Prim(H), the set of all primary La-submodules of H , similar to that for FPrim(F), the spectrum of fuzzy primary ideals of F, and examine the characteristics of this topological space. Particularly, we will research the relation between La-Prim(H) and La-Prim(F/ Ann(H)) and get some results.
Let R be a commutative ring with unity .M an R-Module. M is called coprime module (dual notion of prime module) if ann M =ann M/N for every proper submodule N of M In this paper we study coprime modules we give many basic properties of this concept. Also we give many characterization of it under certain of module.
The problem of finding the cyclic decomposition (c.d.) for the groups ), where prime upper than 9 is determined in this work. Also, we compute the Artin characters (A.ch.) and Artin indicator (A.ind.) for the same groups, we obtain that after computing the conjugacy classes, cyclic subgroups, the ordinary character table (o.ch.ta.) and the rational valued character table for each group.
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In this research the researcher had the concept of uncertainty in terms of types and theories of treatment and measurement as it was taken up are three types of indeterminacy and volatility and inconsistency
Background Over the past decade there has been a growing awareness of, and interest in, the trace element concentration differences between normal and diseased tissues. Significant changes in tissue concentrations of Zinc (Zn) and Copper (Cu) have been previously reported in inflammation and cancer of certain human tissues.
Aim:(1)To correlate between Zn and Cu concentrations and the histological picture of normal and certain inflamed human tissues, namely the gall bladder (GB) the vermiform appendix (VA), visceral adipose tissue (VAT) and subcutaneous adipose tissue (SAT). (2) to detect whether there is a difference in the above-mentioned parameters between VAT and SAT. (3) to obtain recordings for trace element levels in human tissu
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.
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.