Let A, and N  are a semiring ,and  a left A- semimodule, respectively. In this work we will discuss two cases: 

1. The direct summand of π-projective semi module is π-projective, while the direct sum of two π-projective semimodules in general is not π-projective . The details of the proof will be given.
2. We will give a condition under which the direct sum of two π-projective semi modules is π-projective, as well as we also set conditions under which π-projective semi modules are projective.

This paper focuses on developing a strategy to represent the -connected ominoes using an abacus. We use the idea of -connected ominoes with respect to a frame in modelling nested chain abacus. Then, we formulate and prove the unique connected partition for any -connected ominoes. Next, the topological structure of nested chain abacus is presented.

The research focuses,in the first place, on six fields.The most important one is
curriculum field which includes the revision of the current academic curriculums and
substitute them with recent ones, beside the rehabilitation of academic labs and factories by
providing them with modern scientific technologies employed in the world. Regarding the
economical field, it seeks to provide high-level training staffs to serve different social and
economical sectors through modern effective technological and scientific
curriculums.Whereas the social field assures the concern of different social classes who
deprived from the grace of higher education such as retirees and elderly people and to set-up
some educational and ent

Intrinsic viscosities have been studied for polyethylene oxide in water which has wide industrial applications. The polyethylene oxide samples had two different structures, the first one was linear and covers a wide range of molecular weight of 1, 3, 10, 20, 35, 99, 370, 1100, 4600, and 8000 kg/mol and the second one was branched and had molecular weights of 0.55 and 40 kg/mol.
Intrinsic viscosities and Huggins constants have been determined for all types and molecular weights mentioned above at 25ºC using a capillary viscometer. The values of Mark-Houwink parameters (K and a) were equal to 0.0068 ml/g and 0.67 respectively, and have not been published for this range of molecular weight in as yet.

Nilpotency of Centralizers in Prime Rings

Well dispersed Cu2FeSnSe4 (CFTSe) nanofilms were synthesized by hot-injection method. The structural and morphological measurements were characterized using XRD (X-ray diffraction), Raman spectroscopy, SEM (scanning electron microscopy), and TEM (transmission electron microscopy). Chemical composition and optical properties of as-synthesized CFTSe nanoparticles were characterized using EDS (energy dispersive spectroscopy) and UV-Vis spectrophotometry. The average particle size of the nanoparticles was about 7-10 nm. The UV-Vis absorption spectra showed that the synthesized CFTS nanofilms have a band gap (Eg) of about 1.16 eV. Photo-electrochemical characteristics of CFTSe nanoparticles were studied and indicated their potential application

A new definition of a graph called Pure graph of a ring denote Pur(R) was presented , where the vertices of the graph represent the elements of R such that there is an edge between the two vertices ???? and ???? if and only if ????=???????? ???????? ????=????????, denoted by pur(R) . In this work we studied some new properties of pur(R) finally we defined the complement of pur(R) and studied some of it is properties

There are growing concerns over the possibility of transfer genetically modified
sequences from genetically modified feed component (GM feed) to animals and
their products, moreover, affect these sequences on animal and human health. This
study was implemented to detect P35S in modified feed by using PCR technique by
detecting presence P35S promoter, which responsible for the regulation of gene
expression for most of the transgenic genes. Thirty eight feed samples were
collected from different sources of Baghdad markets, which have been used for
feeding livestock, comprise 21 coarse mixes feed, 13 pelleted feed, and 4 expanded
feed. Genomic DNA was extracted by using two methods, CTAB method and
Wizard kit. In

In this paper we introduce the idea of the commutator of two fuzzy subsets of a group and study the concept of the commutator of two fuzzy subsets of a group .We introduce and study some of its properties .