A non-zero submodule N of M is called essential if N L for each non-zero submodule L of M. And a non-zero submodule K of M is called semi-essential if K P for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.
The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl
... Show MoreLet S be a commutative ring with identity, and A is an S-module. This paper introduced an important concept, namely strongly maximal submodule. Some properties and many results were proved as well as the behavior of that concept with its localization was studied and shown.
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 es
... Show MoreLet R1be a commutative2ring with identity and M be a unitary R-module. In this6work we7present almost pure8ideal (submodule) concept as a9generalization of pure10ideal (submodule). lso, we1generalize some9properties of8almost pure ideal (submodule). The 7study is almost regular6ring (R-module).
The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.
The weak and strong forms are so called because it is not their lexical content that primary matter, but the role they have in the sentence. The problematic confusion, our students encounter, in recognizing and producing the correct pronunciation of weak and strong forms of the English function words is the main incentive behind conducting this study. In order to gather the data, this paper used two types of tests: a recognition test and a production test. The general results reached through the analysis of the students' answers seem to conform to the researcher's assumption: students face a critical problem in recognizing and producing correct pronunciation of the weak and strong forms of the English funct
... Show MoreThe main objectives of this research is to extract essential oil from: orange ( citrus sinensis), lemon( citrus limon) and mandarin( citrus reticulata) peels by two methods: steam distillation (SD) and microwave assisted steam distillation (MASD), study the effect of extraction conditions (weight of the sample, extraction time, and microwave power, citrus peel type) on oil yield and compare the results of the two methods, the resulting essential oil was analyzed by Gas Chromatography (GC).
Essential oils are highly concentrated substances used for their flavor and therapeutic or odoriferous properties, in a wide selection of products such as foods, medicines and cosmetics. Extracti
... Show MoreLet Ḿ be a unitary R-module and R is a commutative ring with identity. Our aim in this paper to study the concepts T-ABSO fuzzy ideals, T-ABSO fuzzy submodules and T-ABSO quasi primary fuzzy submodules, also we discuss these concepts in the class of multiplication fuzzy modules and relationships between these concepts. Many new basic properties and characterizations on these concepts are given.
The extraction of Eucalyptus oil from Iraqi Eucalyptus Camadulensis leaves was studded using water distillation methods. The amount of Eucalyptus oil has been determined in a variety of extraction temperature and agitation speed. The effect of water to Eucalyptus leaves (solvent to solid) ratio and particle size of Eucalyptus leaves has been studied in order to evaluate the amount of Eucalyptus oil. The optimum experimental condition for the Eucalyptus oil extraction was established as follows: 100 C extraction temperature, 200 rpm agitation speed; 0.5 cm leave particle size and 6: 1 ml: g amount of water to eucalyptus leaves Ratio.
In the present paper we introduce and study new classes of soft separation axioms in soft bitopological spaces, namely, soft (1,2)*-omega separation axioms and weak soft (1,2)*-omega separation axioms by using the concept of soft (1,2)*-omega open sets. The equivalent definitions and basic properties of these types of soft separation axioms also have been studied.