Let R be an associative ring with identity and M be unital non zero R-module. A
submodule N of a module M is called a δ-small submodule of M (briefly N << M )if
N+X=M for any proper submodule X of M with M/X singular, we have
X=M .
In this work,we study the modules which satisfies the ascending chain condition
(a. c. c.) and descending chain condition (d. c. c.) on this kind of submodules .Then
we generalize this conditions into the rings , in the last section we get same results
on δ- supplement submodules and we discuss some of these results on this types of
submodules.
Abstract:
Most of the studies on this subject, small industrial projects, by researchers and scholars in the economic field show the great and increasing importance of doing this kind of projects, the extent of which can be determined by the contribution of these projects to indicators and macroeconomic and sectorial variables. So this research aims to show the extent of the economic contribution of projects in selected international experiences and in the Iraqi economy. As international experiences have provided the opportunity for the progress and growth of small projects in their economies, which led to an increase in the contribution of these projects in the recruitment of economically active manpower, in added
... Show MoreSolar module operating temperature is the second major factor affects the performance of solar photovoltaic panels after the amount of solar radiation. This paper presents a performance comparison of mono-crystalline Silicon (mc-Si), poly-crystalline Silicon (pc-Si), amorphous Silicon (a-Si) and Cupper Indium Gallium di-selenide (CIGS) photovoltaic technologies under Climate Conditions of Baghdad city. Temperature influence on the solar modules electric output parameters was investigated experimentally and their temperature coefficients was calculated. These temperature coefficients are important for all systems design and sizing. The experimental results revealed that the pc-Si module showed a decrease in open circuit v
... Show MoreLet 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
... Show MoreThe -s-extending modules will be purpose of this paper, a module M is -s-extending if each submodule in M is essential in submodule has a supplement that is direct summand. Initially, we give relation between this concept with weakly supplement extending modules and -supplemented modules. In fact, we gives the following implications:
Lifting modules -supplemented modules -s-extending modules weakly supplement extending modules.
It is also we give examples show that, the converse of this result is not true. Moreover, we study when the converse of this result is true.
Throughout this note, R is commutative ring with identity and M is a unitary R-module. In this paper, we introduce the concept of quasi J- submodules as a – and give some of its basic properties. Using this concept, we define the class of quasi J-regular modules, where an R-module J- module if every submodule of is quasi J-pure. Many results about this concept
Collaborative learning in class‐based teaching presents a challenge for a tutor to ensure every group and individual student has the best learning experience. We present Group Tagging, a web application that supports reflection on collaborative, group‐based classroom activities. Group Tagging provides students with an opportunity to record important moments within the class‐based group work and enables reflection on and promotion of professional skills such as communication, collaboration and critical thinking. After class, students use the tagged clips to create short videos showcasing their group work activities, which can later be reviewed by the teacher. We report on a deployment of Group Tagging in an undergraduate Computing Scie
... Show MoreMalaysia has been supported by one of the high-speed fiber internet connections called TM UniFi. TM UniFi is very familiar to be used as a medium to apply Small Office Home Office (SOHO) concept due to the COVID-19 pandemic. Most of the communication vendors offer varieties of network services to fulfill customers' needs and satisfaction during the pandemic. Quality of Services is queried by most users by the fact of increased on users from time to time. Therefore, it is crucial to know the network performance contrary to the number of devices connected to the TM UniFi network. The main objective of this research is to analyze TM UniFi performance with the impact of multiple device connections or users' services. The study was conducted
... Show MoreIn this reserch Some new substituted and unsubstituted poly imides compounds. were synthesized by reaction of acrylol chloride with different amides (aliphatic and aromatic) in a suitable solvent in the presence amount triethyl amine (Et3N) with heating. The Structure confirmation of all polymers were confirmed using FT-IR,1H-NMR,13C-NMR and UV spectroscopy. Thermal analysis (TG) for some polymers showed their thermal stabilities. Other physical properties including softening points, melting point and solubility of the polymers were also measured
Let be a commutative ring with 1 and be a left unitary . In this paper, the generalizations for the notions of compressible module and retractable module are given.
An is termed to be semi-essentially compressible if can be embedded in every of a non-zero semi-essential submodules. An is termed a semi-essentially retractable module, if for every non-zero semi-essentially submodule of an . Some of their advantages characterizations and examples are given. We also study the relation between these classes and some other classes of modules.
In this paper, we introduced module that satisfying strongly -condition modules and strongly -type modules as generalizations of t-extending. A module is said strongly -condition if for every submodule of has a complement which is fully invariant direct summand. A module is said to be strongly -type modules if every t-closed submodule has a complement which is a fully invariant direct summand. Many characterizations for modules with strongly -condition for strongly -type module are given. Also many connections between these types of module and some related types of modules are investigated.