Let R be a commutative ring with identity, and let M be a unitary (left) R- modul e. The ideal annRM  = {r E R;rm  = 0 V  mE M} plays a central

role  in  our  work.  In  fact,  we  shall  be  concemed   with  the  case  where annR1i1 = annR(x) for   some   x EM such  modules  will  be  called bounded  modules.[t  htrns out that there are many classes of modules properly contained in the class of bounded modules such as cyclic modules, torsion -G·ee modulcs,faithful  multiplicat

In this paper we study the concepts of copure submodules and coregular
modules. Many results related with these concepts are obtained.

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.

Chalcopyrite thin films ternary Silver Indium Diselenide AgInSe2 (AIS) pure and Aluminum Al doped with ratio 0.03 was prepared using thermal evaporation with a vacuum of 7*10-6 torr on glass with (400) nm thickness for study the structural and optical properties. X-ray diffraction was used to show the inflance of Al ratio dopant on structural properties. X-ray diffraction show that thin films AIS pure, Al doped at RT and annealing at 573 K are polycrystalline with tetragonal structure with preferential orientation (112). raise the crystallinity degree. AFM used to study the effect of Al on surfaces roughness and Grain Size Optical properties such as the optical band gap, absorption coefficient, Extinction coefficient, refractive ind

Background/Aim There is an association between patient general health, socioeconomic status and fracture incidence. Aim of this study was to demonstrate the relation between the socioeconomic and health status and the occurrence of fractures in Al-Kindy Hospital residents. Methods A prospective cross-sectional study was performed by using data collected from fractured patients in Al-Kindy Teaching Hospital / Baghdad Orthopaedics Outpatient Clinic, between 12 December 2021 and 8 March 2022. A hundred patients aged 20 to 75 years were included in this study. The data were collected using a researcher-administered questionnaire, which included items to assess patient's socioeconomic status (accommodations, occupation, income status, level of e

This research study examines the impact of information technology on firm profitability and stock returns. Using a comprehensive dataset of firms across various industries, this research employs rigorous statistical analysis techniques to investigate the relationship between IT investments, firm profitability metrics, and stock returns. The study focuses at how IT investments affect financial performance measures including return on assets (ROA) and return on equity (ROE), with P-values of 0.34 and 0.12, respectively. Furthermore, the study investigates the influence of IT on stock returns, taking into account market capitalization, industry trends, and macroeconomic variables. This study's conclusions center on the beneficial assoc

      Let R be a commutative ring with unity. And let E be a unitary R-module. This paper introduces the notion of 2-prime submodules as a generalized concept of 2-prime ideal, where proper submodule H of module F over a ring R is said to be 2-prime if , for r R and x F implies that  or . we prove many properties for this kind of submodules, Let H is a submodule of module F over a ring R then H is a 2-prime submodule if and only if [N ] is a 2-prime submodule of E, where r R. Also, we prove that if F is a non-zero multiplication module, then [K: F] [H: F] for every submodule k of F such that H K. Furthermore, we will study the basic properties of this kind of submodules.

       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.