Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of

     In this paper, we study a new concept of fuzzy sub-module, called  fuzzy socle semi-prime sub-module that is a generalization the concept of semi-prime fuzzy sub-module and fuzzy of approximately semi-prime sub-module in the ordinary sense.  This leads us to introduce level property which studies the relation between the ordinary and fuzzy sense of approximately semi-prime sub-module. Also, some of its characteristics and notions such as the intersection, image and external direct sum of fuzzy socle semi-prime sub-modules are introduced. Furthermore, the relation between the fuzzy socle semi-prime sub-module and other types of fuzzy sub-module presented.

  Let M be an R-module, where R is commutative ring with unity. In this paper we study the behavior of strongly hollow and quasi hollow submodule in the class of strongly comultiplication modules. Beside this we give the relationships between strongly hollow and quasi hollow submodules with V-coprime, coprime, bi-hollow submodules.

Swimming has now become the focus of attention of specialists, which has led to the search for the best methods and various methods of training, which rely heavily on scientific research and studies, through the use of proper planning and a comprehensive scientific and practical vision in the preparation and training process for this game. Some studies have proven that  The use of training methods has a positive role in the athletic training of the swimmer, provided that these methods are used in the correct way according to the scientific principles of training and with the loads and stresses that serve the specialized activity, i.e. the swimming distance. The study aimed at the follow 1- Preparing exercises using elastic ro

مستخلص البحث كان الهدف من البحث هو إعداد تمرينات خاصة لتطوير مهارة التصويب بالقفز بكرة السلة للشباب، إذ لوحظ ضعفاً ملموساً ولاسيما عند فئة الشباب في إحراز النقاط في مهارة التصويب بالقفز المحسوب بنقطتين وذلك لصعوبة أداءه إذ ان المدافعين أصبحوا متمكنين من قدراتهم فضلاً عن عامل الوقت عند الأداء يكاد يكون قليل جداً عند اتخاذ القرار. وقد اعتمد الباحثان في إعداد التمرينات مبدأ التدرج من السهل إلى الصعب والتنوع في

Infertility can be detected when the couples have not completed pregnancy after a year or more of normal coitus. So, in order to treat infertility, there are many supported reproductive techniques are in practice. The success rate of these techniques depends upon the way by which preparation of the paternal semen sample. Over the past 30 years, the manual has been standard as providing global standards and has been used extensively by research and clinical laboratories throughout the world. The spermatozoa of all placental (eutherian) mammals, including humans, are in a protective, no labile formal at ejaculation and are incapable of fertilization even if they are placed in direct contact with an oocyte. Accordingly, they must undergo a sub

In this paper the full stable Banach gamma-algebra modules, fully stable Banach gamma-algebra modules relative to ideal are introduced. Some properties and characterizations of these classes of full stability are studied.