In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout this work, we assume that    is a commutative ring with identity and  is a left unitary R- module. A  proper submodule  of  is called a quasi-radical semi prime submodule (for short Q-rad-semiprime), if     for   ,   ,and then  . Where   is the intersection of all prime submodules of .

In contemporary discourses the debate of most Western thinkers is about the efforts to clarify the normative foundations of democracy. And then, some political thinkers have adopted other models differ in terms of standards for traditional liberal democracy. Be the common goal of democracy will give the formation of a greater role than usual in political liberalism rather than limiting the participatory activity of citizens on the function to give permanent legitimacy to the exercise of state authority. The activity is to be permanently enshrined in the democratic public sphere and the issue must be understood as the source of all political decisions.

          This paper deals with studying the effect of hole inclination angle on computing slip velocity and consequently its effect on lifting capacity. The study concentrates on selected vertical wells in Rumaila field, Southern Iraq. Different methods were used to calculate lifting capacity. Lifting capacity is the most important factor for successful drilling and which reflex on preventing hole problems and reduces drilling costs. Many factors affect computing lifting capacity, so hence the effect of hole inclination angle on lifting capacity will be shown in this study. A statistical approach was used to study the lifting capacity values which deal with the effect of hole

In this paper we introduced a new class of - called - and study their basic properties in nano topological spaces. We also introduce -closure and -interior and study some of their fundamental properties.

Let R be a commutative ring with identity. R is said to be P.P ring if every principle ideal of R is projective. Endo proved that R is P.P ring if and only if Rp is an integral domain for each prime ideal P of R and the total quotient ring Rs of R is regular. Also he proved that R is a semi-hereditary ring if and only if Rp is a valuation domain for each prime ideal P of R and the total quotient Rs of R is regular. , and we study some of properties of these modules. In this paper we study analogue of these results in C.F, C.P, F.G.F, F.G.P R-modules.

In this study, we conducted a series of polymerization studies of hexyl methacrylate in dimethyl sulfoxide with (0.1 - 0.4) mol dm^-3 of monomer and (1 10^-3 – 4 10^-3) mol dm^-3 of benzoyl peroxide as initiators at 70 °C. Using the well-known conversion vs. time technique, the effects of initiator and monomer concentration on the rate of polymerization (R_p) were studied. An initiator of order 0.35 was obtained in accordance with theory and a divergence from normal kinetics was detected with an order of 1.53 with respect to monomer concentration. The activation energy was determined to be (72.90) kJ mol^-1, which does not correspond to the value of most thermally initiated m

Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

Background: - Recurrent breast cancer is cancer that comes back following initial treatment. Risk factors of recurrence are lymph node involvement, larger tumor size, positive or close tumor margins, and lack of radiation treatment following lumpectomy, younger age and inflammatory breast cancer.
Objective: Asses the rate of recurrence for early breast cancer in Iraqi female patients, in relation to certain risk factors.
Patients and methods: A prospective study was conducted on 100 consecutive female patients, with stage I and stage II breast cancer treated by mastectomy and axillary dissection by the same team. Patients were assessed postoperatively every three months and recurrences were detected by physical examination and ultr

     The concept of a small f- subm was presented in a previous study. This work introduced a concept of a hollow f- module, where a module is said to be hollow fuzzy when every subm of it is a small f- subm. Some new types of hollow modules are provided namely, Loc- hollow f- modules as a strength of the hollow module, where every Loc- hollow f- module is a hollow module, but the converse is not true. Many properties and characterizations of these concepts are proved, also the relationship between all these types is researched. Many important results that explain this relationship are demonstrated also several characterizations and properties related to these concepts are given.