Abstract Throughout this paper R represents commutative ring with identity and M is a unitary left R-module, the purpose of this paper is to study a new concept, (up to our knowledge), named St-closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties of St-closed submodules are considered.
In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.
In this paper, we introduce and study the notation of approximaitly quasi-primary submodules of a unitary left -module over a commutative ring with identity. This concept is a generalization of prime and primary submodules, where a proper submodule of an -module is called an approximaitly quasi-primary (for short App-qp) submodule of , if , for , , implies that either or , for some . Many basic properties, examples and characterizations of this concept are introduced.
"In this article, "we introduce the concept of a WE-Prime submodule", as a stronger form of a weakly prime submodule". "And as a "generalization of WE-Prime submodule", we introduce the concept of WE-Semi-Prime submodule, which is also a stronger form of a weakly semi-prime submodule". "Various basic properties of these two concepts are discussed. Furthermore, the relationships between "WE-Prime submodules and weakly prime submodules" and studied". "On the other hand the relation between "WE-Prime submodules and WE-Semi-Prime submodules" are consider". "Also" the relation of "WE-Sime-Prime submodules and weakly semi-prime submodules" are explained. Behind that, some characterizations of these concepts are investigated".
... Show MoreA non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.
Background: The role of prophylactic antibiotics remains controversial. It is clear that actively facial fractures are considered as clean contaminated and should be treated with therapeutic antibiotics; however, there is widespread variability in the use, type, timing, and duration of prophylactic antibiotic administrated in practice today. There is an adverse effect of increased antibiotic resistance, as well as costs, it is important to review the current evidence for the role of prophylactic antibiotics in compound facial fractures. The purpose of this study is to evaluate the role and significance of preoperative, perioperative and postoperative antibiotic prophylaxis for patients when there is already an infective focus, such as co
... Show MoreThe impact of mental training overlap on the development of some closed and open skills in five-aside football for middle school students, Ayad Ali Hussein, Haidar Abedalameer Habe
A submodule N of a module M is said to be s-essential if it has nonzero intersection with any nonzero small submodule in M. In this article, we introduce and study a class of modules in which all its nonzero endomorphisms have non-s-essential kernels, named, strongly -nonsigular. We investigate some properties of strongly -nonsigular modules. Direct summand, direct sums and some connections of such modules are discussed.
Chilled ceilings systems offer potential for overall capital savings. The main aim of the present research is to investigate the thermal performance of the indirect contact closed circuit cooling tower, ICCCCT used with chilled ceiling, to gain a deeper knowledge in this important field of engineering which has been traditionally used in various industrial & HVAC systems. To achieve this study, experimental work were implemented for the ICCCCT use with chilled ceiling. In this study the thermal performances of closed wet cooling tower use with chilled ceiling is experimentally and theoretically investigated. Different experimental tests were conducted by varying the controlling parameters to investigate their effects
... Show MoreIn this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity. A proper submodule of an -module is called an approximaitly prime submodule of (for short app-prime submodule), if when ever , where , , implies that either or . So, an ideal of a ring is called app-prime ideal of if is an app-prime submodule of -module . Several basic properties, characterizations and examples of approximaitly prime submodules were given. Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.