Let R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.

     Let  be an R-module, and let  be a submodule of . A submodule  is called -Small submodule () if for every submodule  of  such that  implies that . In our work we give the definition of -coclosed submodule and -hollow-lifiting modules with many properties.

Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called Z-regular if every cyclic submodule (equivalently every finitely generated) is projective and direct summand. And a module M is F-regular if every submodule of M is pure. In this paper we study a class of modules lies between Z-regular and F-regular module, we call these modules regular modules.

Let R be a commutative ring with identity and let M be a unital left R-module.
A.Tercan introduced the following concept.An R-module M is called a CLSmodule
if every y-closed submodule is a direct summand .The main purpose of this
work is to develop the properties of y-closed submodules.

Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules.

The main purpose of this paper is to develop the properties of Rickart modules .

We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.

A submoduleA of amodule M is said to be strongly pure , if for each finite subset {ai} in A , (equivalently, for each a ?A) there exists ahomomorphism f : M ?A such that f(ai) = ai, ?i(f(a)=a).A module M is said to be strongly F–regular if each submodule of M is strongly pure .The main purpose of this paper is to develop the properties of strongly F–regular modules and study modules with the property that the intersection of any two strongly pure submodules is strongly pure .

Recently, it has been revealed that Toxoplasmosis may be associated with some factors related to type 2 diabetes, such as glucose, insulin, the Homeostatic Model Assessment for Insulin Resistant (HOMA-IR), and Fatty acid binding protein (FABP). Therefore, the current study aimed to specify how Toxoplasma gondii (T.gondii) infection affects glucose, insulin, HOMA-IR, and FABP among adolescents. From October to December 2022, this study was carried out at Al Madain Hospital in Baghdad. For a group of adolescents visiting the hospital, an ELISA test was performed to check their anti-T.gondii antibodies. Ninety adolescents were selected to participate in the study on the basis of this examination. They were divided into two groups: those who te

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.

     The objective of this paper is, first, study a new collection of sets such as field and we discuss the properties of this collection. Second, introduce a new concepts related to the field such as measure on field, outer measure on field and we obtain some important results deals with these concepts. Third, introduce the concept of null-additive on field as a generalization of the concept of measure on field. Furthermore, we establish new concept related to - field noted by weakly null-additive on field as a generalizations of the concepts of measure on and null-additive. Finally, we introduce the restriction of a set function  on field and many of its properties and characterizations are given.

Density Functional Theory (DFT) at the B3LYP/ 6-311G basis set level and
semiemperical methods (PM3, AM1, and MINDO/3) were performed on six new
substituted Schiff bases derivatives of INHC (N-(3-(phenylidene-allylidene)
isonicotinohydrazide) using Gaussian-03 program. The calculated quantum chemical
parameters correlated to the inhibition efficiency were studied and discussed at their
equilibrium geometry and their correct symmetry (Cs). Comparisons of the order of
inhibition efficiency of the Schiff bases derivatives, and local electrophilic and
nucleophilic reactivity have analyzed. Some physical properties also were studied
such as heat of formation, total energy and dipole moment...etc. Also vibration
freq