Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes.
Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ⊊ W ⊆ M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings
... Show MoreThrough this paper R represent a commutative ring with identity and all R-modules are unitary left R-modules. In this work we consider a generalization of the class of essential submodules namely annihilator essential submodules. We study the relation between the submodule and his annihilator and we give some basic properties. Also we introduce the concept of annihilator uniform modules and annihilator maximal submodules.
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.
This paper describes a practical study on the impact of learning's partners, Bluetooth Broadcasting system, interactive board, Real – time response system, notepad, free internet access, computer based examination, and interaction classroom, etc, had on undergraduate student performance, achievement and involving with lectures. The goal of this study is to test the hypothesis that the use of such learning techniques, tools, and strategies to improve student learning especially among the poorest performing students. Also, it gives some kind of practical comparison between the traditional way and interactive way of learning in terms of lectures time, number of tests, types of tests, student's scores, and student's involving with lectures
... Show MoreLet
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Diabetes is a complex set of diseases require continuous medical care, to control blood sugar and prevent complications is .The aim of this research is to determine the effect of administration of L carentin to diabetics on the lipid profile. The research was conducted on sixty diabetic patients were selected from endocrinology and diabetes center / Al-Rusafa, within selected criteria. The patients divided into 3 groups (control group of healthy people and two groups of patients with diabetes who were on metformin and glibenclamide, one group took a L carnitine in a dose of 1000 mg twice daily and a group dealing with a placebo for a period of 3 months continuously). The study found that patients who took Lc
... Show MoreThe marine collagens are biocompatible and biodegradable materials that are considered as a biomimetic approach for tissue regeneration. This study evaluated the effect of daily consumption of marine collagen supplement drink on enamel white spot lesions (WSLs), comparing the results against Regenerate system and Sylc air abrasion methods. Fifty human enamel slabs were allocated into five groups (n = 10 per group): non-treated (sound); non-treated (WSLs, 8% methylcellulose gel with 0.1 M lactic acid (pH 4.6) at 37 °C for 21 days); and three treated surfaces with marine collagen; Regenerate system; and Sylc air abrasion. The treatment lasted for 28 days followed by four weeks’ storage in artificial saliva (pH = 7.0, 37 °C). Evalu
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