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.
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 MoreThe purpose of this paper is to study a new types of compactness in the dual bitopological spaces. We shall introduce the concepts of L-pre- compactness and L-semi-P- compactness .
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The concept of epiform modules is a dual of the notion of monoform modules. In this work we give some properties of this class of modules. Also, we give conditions under which every hollow (copolyform) module is epiform.
Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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Let f and g be a self – maps of a rational exterior space . A natural number m is called a minimal coincidence period of maps f and g if f^m and g^m have a coincidence point which is not coincidence by any earlier iterates. This paper presents a complete description of the set of algebraic coincidence periods for self - maps of a rational exterior space which has rank 2 .
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